1/2 cup warm water (105–115°F)
2 (1/4-oz) packages active dry yeast (5 teaspoons)
1/2 cup granulated sugar
5 cups all-purpose flour plus additional for dusting
1 1/2 teaspoons salt
1 cup warm milk
2 large eggs at room temperature
1 stick (1/2 cup) unsalted butter, softened
1/4 cup water
1 1/3 cups granulated sugar
2 cups fresh or thawed frozen cranberries (9 oz)
1 stick (1/2 cup) unsalted butter, very soft
1/4 cup packed light brown sugar
1 teaspoon cinnamon
1 1/4 cups confectioners sugar
2 tablespoons maple syrup
Make dough: Stir together warm water, yeast, and a pinch of the sugar in a small bowl and let stand until foamy, 5 to 10 minutes. (If mixture doesn’t foam, discard and start over.) Put 5 cups flour, salt, and remaining sugar in bowl of electric mixer and mix with dough hook at low speed until combined. Whisk together milk and eggs in a small bowl, then add to dry ingredients along with yeast, beating at low speed until flour is incorporated. Beat at medium speed until a very soft dough forms, about 2 minutes. Add butter and continue beating at medium speed until dough is smooth, soft, and elastic, about 4 minutes (it will be quite sticky). Spray a large bowl with baking spray. Add dough and cover bowl tightly with plastic wrap. Let dough rise in a warm place until doubled in bulk, 45 minutes to 1 hour.
Prepare filling: Bring water and 1 cup granulated sugar to a boil, stirring until sugar is dissolved. Add cranberries and simmer just until they begin to burst, about 2 minutes. Pour through a large sieve into a bowl and cool berries, reserving syrup for another use (such as a flavoring for seltzer).
Form and bake buns: Turn out dough onto a well-floured surface and dust with flour, then roll out into a 16-inch square. Brush off excess flour, then spread evenly with butter with a small metal offset spatula. Stir together brown sugar, cinnamon, and remaining 1/3 cup granulated sugar and sprinkle evenly over dough. Dot dough evenly with drained cranberries, then sprinkle with nuts if using.
Beginning with side nearest you, roll up dough, firmly but not tightly, into a log, then pinch seam to seal. Trim 1 inch off each end with a large knife and discard, then cut log crosswise into 12 slices. Arrange slices, cut sides up, in buttered cake pans (place 1 slice in center of each pan, then evenly space 5 more around it). Cover with plastic wrap and let rise in a warm place until doubled in bulk, about 1 hour.
Preheat oven to 350°F while buns are rising. Bake buns in lower third of oven until puffed and golden, 30 to 35 minutes, then cool in pan on a rack 10 minutes.
Make glaze: Stir together confectioners sugar and maple syrup with a fork until smooth. Drizzle over buns while still hot. Serve buns warm or at room temperature.