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1
Stir together warm water, yeast, and 1 teaspoon sugar in bowl of mixer fitted with paddle attachment and let stand until foamy, about 5 minutes. (If mixture doesn't foam, discard and start over with new yeast.)
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2
While yeast is foaming, whisk 4 cups flour with zest, salt, and cinnamon in a bowl.
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3
Add milk, vanilla, butter, and remaining 1/2 cup sugar to yeast, then mix at medium speed until combined. Beat in 3 eggs, 1 at a time, then add orange cinnamon flour and mix until combined well.
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4
Replace paddle attachment with dough hook attachment and mix at medium-low speed, adding more flour (1 to 1 1/2 cups), 1/4 cup at a time, until a smooth but slightly sticky dough forms, about 5 minutes. Transfer dough to a work surface and knead by hand until smooth and elastic (dough will remain slightly sticky), about 3 minutes. Form dough into a ball and transfer to a large buttered bowl, turning dough to coat with butter.
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5
Cover bowl with kitchen towel and let dough rise in a draft-free place at warm room temperature until doubled in bulk, 1 1/2 to 2 hours.
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6
Line a 17- by 14-inch baking sheet with parchment paper.
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7
Turn out dough onto work surface and knead several times to remove air. Cut dough into 12 equal pieces. Cup your hand over 1 piece and, using your thumb and pinkie to keep ball inside your cupped hand, push dough with heel of your hand against work surface while rolling in a circular motion (clockwise or counterclockwise) to form a smooth ball. Repeat with remaining pieces of dough, arranging balls 1 inch apart on baking sheet.
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8
Cover loosely with kitchen towel and let dough rise in a draft-free place at warm room temperature until doubled in bulk, 1 to 1 1/4 hours. Put oven rack in middle position and preheat oven to 375u00b0F.
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9
Whisk together remaining egg with remaining 2 teaspoons water in a small bowl. Cut a 1-inch X (1/4 inch deep) in top of each roll with kitchen shears. Brush rolls lightly with egg wash and bake until golden and rolls sound hollow when tapped on bottom, 15 to 20 minutes. Transfer rolls to a rack and cool, at least 15 minutes.
