Pre-heat the oven to 425°F.
Peel and cube the squash and dress with a little EVOO, salt and pepper. Roast until just-tender, 25-30 minutes; do not brown.
After roasting the squash, char the peppers over an open flame on the stovetop or under a hot broiler. Place in a covered dish to cool to handle, then peel, seed and chop.
In a large Dutch oven, heat the EVOO, a couple turns of the pan, and add the fennel, carrots, celery, onions, garlic, chili pepper, salt and pepper, a bundle of rosemary and thyme tied with kitchen twine and two large bay leaves. Cover and cook for 10 minutes, stirring occasionally, to soften. Deglaze the pan with the wine, then add the roasted peppers, tomatoes and a sprinkle of sugar; break up the tomatoes with the back of a spoon and stir in the stock. Bring to a boil, then let simmer at a low rolling boil for 30 minutes. Remove the herb bundle and bay leaves and puree the soup along with the squash in a food processor or industrial blender. Pass through a coarse sieve for a smooth soup.
Wipe out the processor and return it to the base; add the celery tops, fennel fronds, flat leaf parsley, basil or tarragon, nuts and salt and pepper, then turn the processor on. Stream in enough EVOO to form a thick pesto (add a handful of Parmigiano Reggiano if you’d like).
Top shallow bowls of soup with a swirl of pesto. Serve with crusty bread, cheese and herb puffs or grilled cheese sammies.