Brown the butter: set the butter in a light colored frying pan over medium heat. Cook as the butter melts and begins to sputter. Small panko-like bits will fall to the bottom, keep cooking and stirring while those bits turn brown. The butter will smell nutty and it will stop sputtering, going silent as all of the water has evaporated and the milk solids have turned a toasty brown color. Pour into a bowl, scraping up all the brown bits from the pan, and let cool.
Divide the butter: set 113g of the butter (a mix of liquid and brown bits) aside for the filling, 57g (mostly the liquid) for the dough and reserve 1-2 tablespoons of mostly the brown bits for the glaze.
Make the dough: pour the warm water (60g or ¼ cup) into the bowl of a stand mixer. Sprinkle the yeast (2 ¼ teaspoons or 7g) over the water then add a pinch of the sugar. Gently whisk then set aside for a few minutes: it should foam to indicate it’s fresh and good to use. Add the flour on top (520g or 4 cups), along with the pumpkin puree (190g or ¾ cup), greek yogurt (120g or ½ cup), vanilla (1-2 tsp), salt (½ tsp) and the rest of the sugar (100g or ½ cup). Affix the dough hook attachment and begin to knead on low, working up to medium speed. Once the dough starts to come together, pour in the browned butter reserved for the dough (57g or ¼ cup). Knead on medium speed until the dough clears the bowl and forms a lump around the hook. Transfer the dough to the counter and knead by hand for a few minutes, until supple. Transfer to an oiled bowl and cover with plastic wrap to seal.
First rise: leave the dough at room temperature until roughly doubled in size, 2-3 hours depending on the temperature of the kitchen. If you are letting the dough rise overnight, it should only increase by 50% before placing in the fridge (about 1-2 hours at room temperature).
Fill the dough: On a well floured countertop, roll the dough out to a large rectangle that’s about 14 inches x 12 inches. Spread the cooled (it should be at a creamy consistency, cooled but not solid) browned butter reserved for the filling over the dough (113g or ½ cup). In a separate bowl, mix together the brown sugar (150g or ¾ cup) with the pumpkin spice (1-2 tablespoons) and the fine sea salt (¼ tsp). Sprinkle this mix over the butter, spreading with an offset spatula or your hand into an even layer. Roll up the dough so you have a long rope then slice it using a bread knife, into 10-12 rolls (depending how large you want them).
Second rise: oil or butter a 13 x 9 inch cake pan and arrange the unbaked rolls in the pan so they have enough room to spread and rise; about half an inch of space around each. Cover the pan with the plastic wrap or a tea towel and let rise at room temperature until puffy and when pressed, the dough leaves an indentation - about 1-2 hours (longer if the dough was in the fridge overnight).
Bathe and bake: Preheat the oven to 350 F. Pour the heavy cream (120g or ½ cup)around and in the space between the rolls. Tilt the pan so the heavy cream covers the pan where it is visible. Bake the rolls until golden brown, about 25-35 minutes. You can check for doneness by using an instant read thermometer, inserted into the middle of the middle roll it should reach 190 F.
Top the rolls: in a bowl, whisk together the reserved brown butter bits (1-2 tablespoons), the powdered sugar (190g or 1 ½ cups), vanilla (1-2 teaspoons), a pinch of salt, heavy cream or milk (2-4 tablespoons). Add the cream cheese if using. Whisk until the glaze is smooth; thick but spreadable. Spread the glaze over the rolls: if you like it to melt all over the rolls do this while they are still warm. If you prefer a thicker topping that stays separate from the bottom rolls, wait until they are completely cool then spread the glaze.