In a large Dutch oven, heat 3 tablespoons EVOO over medium-high heat. Add fennel, carrots, celery, onions, garlic, chili, salt and pepper. Bundle the rosemary and thyme and tie together with kitchen twine. Add the herbs and bay leaves to the pot, cover and cook 10 minutes, stirring occasionally, until soft. Deglaze pan with wine, add in roasted red peppers, tomatoes and sugar. Break up tomatoes with a spoon, stir in stock and bring to boil. Reduce heat and simmer at low rolling boil for 30 minutes.
Remove herb bundle and bay, puree soup along with squash in a food processor or industrial blender. Pass through coarse sieve for a smooth soup.
Wipe out processor and return to base. Add celery tops, fennel fronds, parsley, basil or tarragon, nuts, salt and pepper. Turn processor on and stream in enough EVOO to form a thick pesto. (Add a handful of Parmigiano-Reggiano if ya like.)
Top shallow bowls of soup with a swirl of pesto. Serve with crusty bread, gougeres or grilled cheese sammies.