For the romesco sauce: Toast the chile peppers in a small pot over medium heat, pressing them flat with a metal spatula and turning occasionally. Add enough water or stock to cover and simmer until the chiles are tender. Transfer the chiles to a food processor with a splash of the cooking liquid. Add the almonds, hazelnuts, paprika, piquillos, bread, garlic, tomato, vinegar and some salt and pepper. Turn the processor on and add the EVOO in a slow, steady stream until a thick, almost smooth sauce forms.
For the stew: Heat the EVOO in a pot over medium to medium-high heat. Add the potatoes and season with salt and pepper. Cook until lightly browned, then add the celery, bay leaf, onions and parsley bundle and cook for 5 minutes. Deglaze with the wine, stirring and scraping up any browned bits from the bottom of the pot with a wooden spoon. Stir in the stock and romesco sauce. Bring to a simmer and cook until the potatoes are just tender.
For the seafood: Add the mussels and shrimp to the stew and cook, covered, until the mussels open and the shrimp are firm and opaque. Discard any unopened shells.
Meanwhile, preheat the oven to 375 degrees F.
Heat a drizzle of EVOO in a nonstick skillet over medium-high heat. Wrap the ham around the fish fillets, then add to the skillet and cook until crisp on both sides, about 2 minutes per side. Transfer the skillet to the oven and roast until the fish is cooked through, about 5 minutes. Remove from the oven and let the fish rest in the skillet. Meanwhile, char the bread in the oven. Divide the stew among shallow bowls. Place a piece of fish in the center and top with a spoonful of Gremolata. Rub the charred bread with the cut sides of the garlic clove and drizzle with EVOO; serve on the side.
Pile the parsley, thyme, anchovy, garlic and lemon zest on a cutting board and roughly chop together until well combined.
You can make extra romesco sauce and freeze it. Use it as a base for soup or for topping any grilled or roasted meat or seafood. The stew, without the seafood, can be covered and refrigerated for a make-ahead meal.