For the pumpkin rolls, stir the yeast into the lukewarm milk in a small bowl. Allow the mixture to rest at room temperature for 5 minutes.
In the bowl of an electric mixer fitted with the paddle attachment, mix together the flour, pumpkin, butter, sugars, eggs, salt, cinnamon, nutmeg, cloves and milk mixture at medium low speed until a rough dough forms. Knead the dough by hand or with the dough hook attachment of your stand mixer until smooth and cohesive. Place the dough in a clean and lightly-greased bowl. Cover with a kitchen towel and allow to rise at room temperature out of direct sunlight until doubled in size, about 1 hour.
Roll out the dough into a rectangle until the dough is about 1/4 inch thick. For the cinnamon filling, spread the softened butter across the top of the dough, and then sprinkle the brown sugar and cinnamon over it. Use a pizza cutter to cut the dough into 12 strips, each roughly 1-inch wide (it’s okay if they’re a bit wider, there just need to be 12 of them total).
Roll each strip into a little roll. Lay the roll down and pat it gently a couple times to help secure the layers together. Place each of the 12 cinnamon rolls into an individual muffin cup in a well-greased muffin pan. Cover and allow to rise at room temperature out of direct sunlight until the rolls are puffy, about 30 minutes to 1 hour.
Preheat the oven to 400 degrees Fahrenheit. Remove the cover and bake the rolls until golden, about 15-20 minutes. Remove the pan from the oven and allow them to cool for 20 minutes.
While the rolls are cooling, make the maple glaze. Whisk together the powdered sugar, milk, maple syrup, and maple extract until smooth. Drizzle the glaze over the top of the cooled pumpkin cinnamon rolls. Serve any leftover glaze alongside the rolls for dipping.