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