In a bowl, combine both paprikas with the vinegar and olive oil and season with salt and pepper. In another bowl, combine both bell peppers with the shallot and 1/4 cup of the paprika vinaigrette; reserve the remaining vinaigrette. Let the pepper mixture stand at room temperature for 15 minutes.
Using a very sharp knife, slice the squid bodies crosswise 1/8 inch thick. Oil a large rimmed baking sheet and, using a long spatula, carefully transfer the squid to the sheet, keeping the shape of the squid as intact as possible.
Preheat the broiler. Brush the squid generously with some of the reserved vinaigrette and season with salt and pepper. Broil the squid 4 inches from the heat for about 2 minutes, until just tender and glazed.
Meanwhile, toss the mesclun with the remaining vinaigrette and arrange on plates. Transfer the squid to the plates, keeping the shape intact. Dot the marinated pepper mixture around the salad and serve.
Mencía is a natural match for the smoked-paprika vinaigrette brushed on the squid.