Pull-Apart Bread with Pumpkin and Spinach

Mix flour, pumpkin, milk, sugar, yeast, nutmeg, 2 Tbsp. butter, and 1 tsp. kosher salt in a large bowl or the bowl of a stand mixer fitted with the dough hook until dough comes together. Knead with your hands or dough hook until dough is soft and smooth, about 10 minutes. Form into a ball.
Lightly grease a large clean bowl with oil; transfer dough to bowl. Cover tightly with plastic wrap and let rise in a warm place until doubled in size, about 1 hour.
Meanwhile, purée cheese, spinach, pepper, garlic powder, 5 Tbsp. butter, and remaining 1/4 tsp. kosher salt in a food processor until smooth. Add egg and pulse to combine.
Arrange racks in upper and lower thirds of oven; preheat to 375°F. Divide dough into 2 equal pieces. Roll each piece to a 14x8" oval.
Transfer 1 oval to a parchment-lined baking sheet. Spread half of spinach mixture in a thin layer over. Starting at long side, tightly roll dough around filling into a long tube (like a cinnamon roll).
Arrange tube diagonally on sheet. Starting 1" from end closest to you, use sharp kitchen shears to make a deep incision at a 45-degree angle away from you, cutting almost to the bottom without cutting through. Carefully shift small cut piece to the left, keeping the bottom connected. Make another 45-degree incision 1" from first. Carefully shift piece to the right. Continue cutting and shifting to alternate sides for a total of 12-14 pieces. Repeat rolling, filling, and cutting with second piece of dough on another parchment-lined rimmed baking sheet.
Brush dough with 2 Tbsp. butter; sprinkle edges with sea salt. Bake, rotating sheets halfway through, until golden brown, 25-30 minutes.
Brush bread with remaining 1 Tbsp. butter and let cool slightly before serving.
Dough and filling can be made 1 day ahead; cover and chill. Bring to room temperature before rolling and filling.