Lightly brush a large bowl with butter, and set aside.
Heat milk and 3 tablespoons of butter in a small saucepan over medium heat until the butter is melted and the mixture is warm to the touch (about 120 degrees).
Transfer to the bowl of a stand mixer fitted with the dough hook attachment. Sprinkle yeast on immediately.
Let stand until it is a bit foamy (about 5 minutes).
Add flour, granulated sugar, egg, apple, pumpkin and 1 teaspoon of salt.
Mix on medium-low speed, scraping the sides and bottom of the bowl once, until the dough is smooth and elastic (about 7 minutes).
Transfer to a bowl and cover tightly with plastic wrap. Let it rise in a warm place until doubled in size (about 1-2 hours)
Brush a 9x13 baking dish with butter, and set aside.
In a medium bowl, stir together the remaining stick of melted butter, brown sugar, cinnamon and a large pinch of salt until smooth and fluffy. Set aside.
Transfer dough to a lightly floured work surface.
Roll out to a 15x12 inch rectangle.
Spread the butter mixture over the dough, leaving a ¼ inch border.
Starting at a long edge, roll up the dough like a jelly roll, then cut crosswise into 15 pieces.
Place pieces in a pan, cut-side up, spaced evenly.
Cover tightly with plastic wrap and let rise in a warm place until the buns are almost doubled in size (about 45-60 minutes)
Preheat oven to 350 degrees. Bake buns until golden brown and topping is bubbling around the sides of the pan (about 17-20 minutes).
Let cool in a pan on a wire rack (10 minutes)