For the Dough:
2 3/4 cups plus 2 tablespoons all-purpose flour
1/4 cup granulated sugar
2 1/4 teaspoons (1 envelope) active dry yeast
1/2 teaspoon salt
2 ounces unsalted butter
1/3 cup whole milk
1/4 cup water
2 large eggs, at room temperature
1 teaspoon pure vanilla extract

For the Filling:
1 cup granulated sugar
2 teaspoons ground cinnamon
1/2 teaspoon fresh ground nutmeg
2 ounces unsalted butter, melted until browned