In the bowl of a stand mixer, combine the yeast, maple syrup, and warm milk. Let sit 5-10 minutes, until bubbly.
With a dough hook attached, mix in 4 tablespoons of salted butter and the pumpkin puree. On low speed, knead in 3 cups of the flour, cinnamon, ginger, and salt. Add additional flour 1/4 cup at a time until a soft, cohesive dough forms. It should be tacky, but not sticky. Continue kneading the dough for 5-10 more minutes. You may use up to 4 1/2 cups to create the right texture.
Lightly grease the mixing bowl with oil or butter. Turn the dough ball so both sides are coated. Cover with plastic wrap or a clean tea towel and let rise until doubled, about 1 hour.
While the dough rises, make the sage butter. Melt 2 tablespoons of butter and the sage leaves in a skillet over medium heat until the butter is golden brown and the sage leaves crisp, about 3-4 minutes. Move the sage leaves to a plate lined with paper towels to drain. Let the butter cool, then chop the sage and stir the browned butter and sage leaves into the remaining 4 tablespoons of butter.
Grease a large 9 x 13 inch casserole dish or cake pan with oil or butter.
Punch down the dough and divide in half. Flour a clean work surface and roll the dough into a 1/4 inch thick square. Cut into 6 strips. Brush the length of each strip with the sage butter and, starting from the short end, roll tightly down the entire length. See photos for reference. Set each roll seam-side down into the casserole dish with about 1/2 inch or so between each. Repeat with the remaining ball of dough. Cover the dish and let the rolls rise for 30 minutes.
Preheat oven to 400 degrees. Uncover the rolls and brush the tops with the remaining sage butter. Bake for 15-18 minutes until golden and puffy.
For the maple butter, stir the butter, maple syrup, and salt until combined. Serve the rolls warm with maple butter and a sprinkle of flaky salt.