In a stand mixer bowl, whisk flour, sugar, salt, and yeast. Separately whisk warm milk, melted butter, pumpkin, and egg. Combine and knead with dough hook 8 to 10 minutes until smooth and slightly tacky.

Shape dough into a ball, place in a greased bowl, cover, and let rise until doubled, 1 to 1 1/2 hours. Punch down.

On a floured surface, roll dough into a 12x18-inch rectangle. Spread the 3 tablespoons soft butter over the surface, then evenly sprinkle with brown sugar, cinnamon, and pumpkin pie spice.

Cut lengthwise into 6 strips, stack them, and cut crosswise into 6 stacks. Arrange the stacks in a buttered 9x5-inch loaf pan with cut edges up. Cover and let rise 30 to 45 minutes until puffy.

Preheat oven to 350°F (175°C). Bake loaf 30 to 35 minutes until deep golden and an internal temperature of 190°F. Cool in pan 10 minutes, then turn out onto a wire rack.

Whisk powdered sugar, maple syrup, and enough milk to form a thick glaze. Drizzle over the warm loaf and serve.