For the Buns• 1 cup whole milk (236ml)• ⅓ cup water (78ml)• 2 ¼ teaspoons active dry yeast (7g)• ⅓ cup granulated sugar• 5 Tbsp unsalted butter melted (70g)• 1 large egg + 1 large egg yolk room temperature preferred• 2 teaspoons table salt• ¼ tsp nutmeg optional• 4-5 cups all-purpose or bread flour plus additional as needed (500-625g, + additional as needed)
For the Filling• 4 Tablespoons unsalted butter very soft (56g)• ½ cup light or dark brown sugar firmly packed (100g)• 2 teaspoons ground cinnamon• ⅛ teaspoon allspice optional but recommended• ⅛ teaspoon ground nutmeg optional but recommended• ⅛ teaspoon table salt• 2 ½ cups chopped peeled/cored apple (280g)
For the Caramel Glaze• ¾ cups dark brown sugar firmly packed (150g)• ½ cup unsalted butter cut into 8 pieces (113g)• ⅓ cup whole milk (78ml)• ¼ teaspoon salt• ½ cup powdered sugar (63g)• ½ teaspoon vanilla extract
Combine milk and water in a heatproof container and heat until 110-120F (43-49C). Pour into a large mixing bowl, sprinkle yeast overtop and add a pinch of your granulated sugar.
While stirring, gradually add additional flour until the dough clings to itself and pulls from the sides of the bowl. Stir until dough is still a bit tacky to the touch but not too sticky.
Place dough in a large, lightly oiled bowl and turn to coat the surface with a thin layer of oil. Cover tightly and place in a warm place to rise until doubled in size ( 1-2 hours).
Cover rolls with a towel and place in a warm spot to rise until puffed and increased in size at least 50%, about 25-40 minutes. Meanwhile, preheat oven to 350F (175C).
Combine brown sugar, butter, milk, and salt in a saucepan over medium heat. Cook until butter is melted and sugar dissolves. Boil for 5 mins, stirring frequently.