Brown the butter by melting it in a light-colored skillet. Cook the butter, stirring constantly, until it becomes foamy and the milk solids separate and settle on the bottom of the pan. Continue to cook until some foam subsides and the milk solids are brown and the butter smells intensely nutty. Immediately transfer the butter to a glass bowl and place it in the refrigerator or freezer until it is no longer warm to the touch, but still liquid.

Add the milk, yeast, pumpkin, brown butter (reserve 2 tablespoons for later use), brown sugar, egg, sage, thyme, pumpkin pie spice, and salt to the bowl of a stand mixer fitted with a whisk attachment and mix until combined.

Add 2 cups of flour and mix to combine. Swap the whisk attachment for the dough hook. Keep adding flour, half a cup at a time and mix on medium low until a soft dough forms. If the dough appears too sticky or dry, add a small amount of flour or milk until the desired texture is reached.

Knead the dough with the dough hook for 5 to 6 minutes until slightly sticky but pulling away from the sides. The dough should be fairly soft after kneading. Poke the dough with your finger and if it slowly bounces back it's ready to rise.

Shape the dough into a ball and place it in a large bowl coated with olive oil. Cover the bowl with a tea towel or plastic wrap and rise for about an hour until doubled in size.

Gently punch the dough down to release air. Pinch off 12 to 16 pieces of dough (depending on how large you want your rolls to be), shape them into balls by stretching the tops and pinching the bottoms, and place them in a buttered 9 x 13 baking dish. Cover the rolls and rise in a warm spot for about another 30 minutes until doubled in size.

Meanwhile, preheat your oven to 350°F. Bake the rolls for 20 to 25 minutes until golden brown.

Melt the reserved brown butter for a few seconds in the microwave and mix in some fresh chopped sage. Brush the tops of the warm rolls with the butter and finish with a sprinkle of flaky salt. Enjoy warm.