Heat a small saucepan over medium heat with the EVOO, 1 turn of the pan. Add the garlic and shallot and cook until softened, about 2 minutes. Add the piquillo peppers and heat for 1 minute. Add the Sherry and cook for 30 seconds. Transfer to a food processor with 1/4 cup broth and puree until smooth; return to the pan.
Add the squash and the remaining 3/4 cup chicken broth to the soup. Whisk to combine. Season to taste with salt, pepper and hot sauce and simmer for a few minutes. Stir in the cream and simmer for 1 minute. Serve the soup in espresso cups topped with the pumpkin seeds and parsley.