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For the dough:.
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In bowl of standing mixer, whisk eggs to combine; add buttermilk and whisk to combine.
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Whisk in sugar, salt, and yeast.
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Add about 2 cups flour and butter; stir with wooden spoon or rubber spatula until evenly moistened and combined.
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Add all but about 1/4 cup remaining flour and knead with dough hook at low speed 5 minutes. Check consistency of dough (dough should feel soft and moist but should not be wet and sticky; add more flour, if necessary); knead at low speed 5 minutes longer (dough should clear sides of bowl but stick to bottom).
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Turn dough out onto lightly floured work surface; knead by hand about 1 minute to ensure that dough is uniform (dough should not stick to work surface during hand kneading; if it does stick, knead in additional flour 1 tablespoon at a time).
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Lightly spray large bowl or plastic container with nonstick cooking spray.
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Transfer dough to bowl, spray dough lightly with cooking spray, then cover bowl tightly with plastic wrap and set in warm, draftfree spot until doubled in volume, 2 to 2 1/2 hours.
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For the glaze:
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Meanwhile, combine all ingredients for glaze in small saucepan; cook over medium heat, whisking occasionally, until butter is melted and mixture is thoroughly combined.
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Pour mixture into nonstick metal 13- by 9-inch baking dish; using rubber spatula, spread mixture to cover surface of baking dish.
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Set baking dish aside.
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To assemble and bake buns:
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For filling, combine brown sugar, cinnamon, cloves, and salt in small bowl and mix until thoroughly combined, using fingers to break up sugar lumps; set aside.
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Turn dough out onto lightly floured work surface.
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Gently shape dough into rough rectangle with long side nearest you.
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Lightly flour dough and roll to 16- by 12-inch rectangle.
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Brush dough with 1 tablespoon melted butter, leaving 1/2-inch border along top edge; with butter remaining on brush, brush sides of baking dish.
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Sprinkle filling mixture over dough, leaving 3/4-inch border along top edge; smooth filling in even layer with hand, then gently press mixture into dough to adhere.
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Beginning with long edge nearest you, roll dough into taut cylinder. Firmly pinch seam to seal and roll cylinder seam-side down.
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Very gently stretch to cylinder of even diameter and 18-inch length; push ends in to create even thickness.
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Using serrated knife and gentle sawing motion, slice cylinder in half, then slice each half in half again to create evenly sized quarters.
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Slice each quarter evenly into thirds, yielding 12 buns (end pieces may be slightly smaller).
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5Arrange buns cut-side down in prepared baking dish; cover tightly with plastic wrap and refrigerate 10 to 14 hours.
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Place baking pan in warm-water bath (about 120 degrees) in kitchen sink or large roasting pan for 20 minutes.
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Remove from water bath and let stand at room temperature until buns look slightly puffy and are pressed against one another, about 1 1/2 hours.
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About an hour before baking, adjust oven rack to lowest position, place pizza stone on rack (if using), and heat oven to 350 degrees.
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Place baking pan on pizza stone; bake until golden brown and center of dough registers about 180 degrees on instant-read thermometer, 25 to 30 minutes.
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Cool on wire rack 10 minutes; invert onto rimmed baking sheet, large rectangular platter, or cutting board. With rubber spatula, scrape any glaze remaining in baking pan onto buns; let cool while making pecan topping.
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For the topping:
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Combine butter, brown sugar, corn syrup, and salt in small saucepan and bring to simmer over medium heat, whisking occasionally to thoroughly combine.
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Off heat, stir in vanilla and pecans until pecans are evenly coated. Using soup spoon, spoon heaping tablespoon nuts and topping over center of each sticky bun.
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Continue to cool until sticky buns are warm, 15 to 20 minutes. Pull apart or use serrated knife to cut apart sticky buns; serve.