Sweet or Savory Dampfnudel
1 cup milk 1 cup milk, or as needed 1 cup warm milk 1 dash vanilla extract, or to taste 1 tablespoon unsalted butter 1 teaspoon brandy, or to taste 1 teaspoon salt 1 teaspoon vanilla extract 1 ½ (.25 ounce) packages active dry yeast 2 cups white sugar 2 eggs 2 tablespoons all-purpose flour 2 tablespoons unsalted butter 3 cups all-purpose flour, or more as needed 3 tablespoons butter, or as needed ¼ cup butter, softened ¼ cup white sugar ¼ cup white sugar, or as needed ½ cup heavy whipping cream ½ cup maple syrup ½ cup warm water, divided ½ cup white sugar