For the Dough:
1 cup whole milk
1 1/4-ounce packet active dry yeast
1/4 cup plus 1/4 teaspoon granulated sugar
4 tablespoons unsalted butter, melted, plus more for the bowl
1 large egg yolk
1 1/2 teaspoons vanilla extract
2 3/4 cups all-purpose flour, plus more if needed
3/4 teaspoon salt
1/2 teaspoon freshly grated nutmeg
For the Filling:
• All-purpose flour, for dusting
• 12 tablespoons unsalted butter, softened, plus more for the pan
• 1/2 cup granulated sugar
• 3 tablespoons ground cinnamon
For the Glaze:
• 2 cups confectioners’ sugar
• 1/3 cup heavy cream
• 4 tablespoons unsalted butter, melted
Make the dough: Warm the milk in a medium saucepan over low heat until it reaches about 100. Remove from the heat and sprinkle in the yeast and 1/4 teaspoon sugar (don’t stir). Set aside until foamy, 5 minutes. Whisk in the melted butter, egg yolk and vanilla.
Whisk the flour, the remaining 1/4 cup sugar, the salt and nutmeg in the bowl of a stand mixer. Make a well in the center and pour in the yeast mixture. Mix on low speed with the dough hook until thick and slightly sticky. Knead on medium speed until the dough gathers around the hook, 6 minutes. (Add up to 2 more tablespoons flour if necessary.)
Remove the dough and shape into a ball. Butter the mixer bowl and return the dough to the bowl, turning to coat with butter. Cover with plastic wrap and let rise until doubled, 1 hour 15 minutes.
Roll out the dough, fill and cut into buns (see instructions below). Butter a 9-by-13-inch baking pan; place the buns cut-side down in the pan, leaving space between each. Cover with plastic wrap and let rise until doubled, 40 minutes. Preheat the oven to 325.
Bake the buns until golden brown, about 35 minutes. Cool in the pan 15 minutes. Meanwhile, make the glaze: Sift the confectioners’ sugar into a bowl, then whisk in the cream and melted butter. Transfer the buns to a rack and spoon the glaze on top while still warm.
How to Form Cinnamon Buns
1. On a lightly floured surface, roll the dough into a 12-by-14-inch rectangle with the longer side facing you.
2. Spread with the softened butter, leaving a 1/2-inch border on the far long edge. Mix the sugar and cinnamon; sprinkle over the butter.
3. Brush the unbuttered far edge with water. Roll the dough away from you into a tight cylinder and press on the long edge to seal.
4. Cut the cylinder with a sharp knife to make 6 equal-size buns.