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1
Make the dough the day before you want to make the rolls. In the bowl of an electric mixer fitted with the dough hook, mix the flour, sugar, yeast, and salt to combine.
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2
Add the eggs and milk and mix on low speed until the mixture forms a ball around the hook, about 4 minutes. Increase the speed to medium and mix until the dough is very smooth, 5 more minutes.
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3
Continue mixing the dough on medium speed and add the butter 1 tablespoon at a time, mixing well to incorporate after each addition. All of the butter should be added over about 3 minutes of mixing.
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4
Transfer the dough to a large, oiled bowl and let rise at room temperature, covered, for 1 to 1 1/2 hours. The dough is very enriched, so it may not expand much.
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5
While the dough rises, prepare the peach butter. In a large pot, combine the peaches, sugar, honey, vanilla bean, cinnamon, nutmeg, salt, and vinegar. Heat the mixture, stirring occasionally, until the peaches are very tender and begin to break down, about 25 to 30 minutes. Remove the vanilla bean and discard.
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6
Use a hand blender, blender, or food processor to process the mixture until it's smooth, then return to the pot and continue to cook until the mixture thickens slightly, 30 to 45 minutes more. Stir in the almond extract, if using. Refrigerate overnight.
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7
Transfer the dough to a parchment-lined baking sheet and pat out into a rectangle with about 1-inch thickness. Cover directly with plastic wrap and refrigerate overnight.
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8
The next day, preheat the oven to 375u00b0 F. Grease a large casserole or 9 x 13-inch baking dish generously with softened butter.
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9
Lightly flour your work surface, then turn the dough out onto it. Remove the parchment from the dough, and flour the top surface of the dough. If the dough feels particularly sticky (sometimes in the summer it can give you a little trouble since it's so rich and buttery!), you can pat it out on parchment paper. Use your hands to pat out the dough into a rectangle about 1/2-inch thick (it should be about 10 x 15 inches). If the dough feels really soft at this point, refrigerate it to firm it up before proceeding (5 to 10 minutes).
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10
In a medium bowl, whisk the chilled peach butter with the 1/3 cup flour to combine. Spread the filling in an even layer all over the dough-all the way to the edges!
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11
Starting with one of the long sides, begin to roll the dough into a tight spiral (if you're using parchment, you can use it to help you roll the dough up, too). Use your thumbs to prop the dough off the work surface and use your fingers to keep the roll tight while you work. If the dough feels really soft at this point, you can refrigerate it again before slicing (10 to 15 minutes).
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12
Slice the finished roll into 9 even pieces (these are big rolls). Arrange the rolls inside the prepared baking dish, leaving about 1/4 inch between each one. Cover the rolls loosely with plastic wrap or a clean kitchen towel and let rise in a warm place for about 30 minutes.
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13
Brush the top of the rolls with egg wash and bake until they are golden on the surface and the filling is bubbly, about 35 to 40 minutes.
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14
While the rolls bake, whisk the powdered sugar, cream, and vanilla to combine.
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15
When the rolls are baked, let them cool for 10 to 15 minutes, then spread or drizzle the icing on top. Serve warm.
