In a large bowl, or the bowl of a stand mixer, stir the warm water, yeast, and sugar. Let sit for 5-10 minutes to activate the yeast. Once the yeast has foamed, mix in the maple syrup, salt, oil, and pumpkin puree.
Now, mix in 2 cups of flour until fully incorporated. Then mix in another 1 cup for a total of 3 cups.
Use the last cup of flour to dust your hands and the dough throughout the kneading process. Lightly knead the dough until a slightly sticky dough ball forms, this should take about 2-3 minutes. (You may not need the full cup of flour. I use anywhere from ¼-3/4 cups of it.)
Once the dough comes together shape it into a ball. Then, lightly coat the bowl and the dough with a bit of oil. Cover with a kitchen towel and set aside to rise for 45 minutes.
To Shape the Rolls
Turn out the risen dough onto a floured surface. Depending on the size of rolls you want, cut the dough into 9, 12, or 16 evenly-sized pieces.
Form each piece into a ball by pulling and tucking the edges of the dough underneath itself. Gently roll the dough ball, seam side down, on a clean dry surface to create a smooth ball.
Transfer rolls to a lightly oiled oven-safe dish.
Cover with a kitchen towel and allow the rolls to rise for another 30-45 minutes.
To Bake
Once the rolls have doubled in size, bake at 400ºF for 14-20 minutes or until the tops brown.
Brush the warm rolls with oil or vegan butter and sprinkle with coarse sea salt.
Notes
To skip oiling the tops of the rolls, you can add the salt to the top of the dough just before baking. The salt will bake into the rolls and stick. However, the top of the rolls won't be as glossy.
For an extra touch of fall flavor, add 1-2 teaspoons of pumpkin spice.