In a large bowl, combine warm water, 1 tbsp brown sugar, and yeast. Stir and let sit for 5–10 minutes, until foamy.
Add pumpkin purée, remaining 2 tbsp brown sugar, salt, 1 tsp cinnamon, and nutmeg. Stir in flour gradually until a sticky dough forms.
Cover the bowl with plastic wrap or a towel and let the dough rise at room temperature for about 1 hour. After 40 minutes, place your Dutch oven (with lid) inside the oven and preheat to 450°F.
In a small bowl, mix 2 tbsp brown sugar with 1–1½ tsp cinnamon. Turn the risen dough onto a floured surface and gently flatten into a rectangle. Brush with softened butter, sprinkle evenly with the cinnamon-sugar mixture, then roll up jelly-roll style. Tuck ends under to form a round loaf.
Second Rise: Place the dough seam-side down on parchment in a bowl. Cover and let rest for 30 minutes.
Carefully lower the dough on the parchment into the preheated Dutch oven. Cover and bake for 30 minutes. Remove the lid and bake uncovered for another 5–10 minutes, until golden brown.
Let cool at least 30 minutes before slicing to allow the swirl to set.