Snap the stems from the chiles. Shake out and discard the seeds. Put the chiles in a heatproof bowl and cover with 2 cups boiling water. Set a small plate on top to keep the peppers submerged and let sit until softened, about 20 minutes. Discard the soaking liquid. Set the peppers aside.
Roast the red bell peppers: On the stovetop, hold the peppers with tongs over an open burner, turning them until they’re blackened uniformly, about 3 to 5 minutes. (Alternatively, put the peppers on a baking sheet and roast in the oven at 450°F until the skins become brown and loosen, about 30 minutes.) Transfer to a bowl and cover tightly with plastic wrap for 15 minutes, allowing them to steam and cool slightly. Peel the skins from the peppers, remove the seeds, and set the peppers aside.
Heat 2 Tbs. of the olive oil in a small skillet over medium heat, then add the hazelnuts and cook, shaking the pan a few times, until lightly browned, about 4 minutes. Drain the hazelnuts and let cool slightly. Remove as much paper coating on the nuts as possible. Discard the oil.
Make the romesco sauce: Combine the chiles, roasted red bell peppers, hazelnuts, breadcrumbs, garlic, tomatoes, sherry vinegar, and 1/2 cup olive oil in the bowl of a food processor. Season generously with salt and pepper and pulse until completely puréed. Transfer to a small plastic container, cover, and refrigerate until needed. The romesco can be made a day ahead and kept covered in the refrigerator.
Heat the remaining 1/4 cup olive oil in a large straight-sided skillet over high heat. Add the shrimp, season with salt and pepper, and cook until the shrimp turn pink and become firm, about 1 to 2 minutes per side.
Warm the cold romesco sauce. Transfer the shrimp to a serving platter and serve the romesco sauce on the side. Garnish with the chopped parsley and serve immediately.