In a food processor, pulse the peppers, 3 tbsp. oil, the hazelnuts, tomato paste, vinegar, garlic and paprika to a coarse puree. Season with salt and pepper.
In a large pot of boiling, salted water, cook the green beans until bright green, 2 to 3 minutes; transfer to a large bowl of ice water. Let cool, then drain and pat dry.
In a large nonstick skillet, heat 1 tbsp. oil over medium. Add the shallot and cook, stirring often, until softened, 1 to 2 minutes. Add the green beans, season and cook, stirring often, until crisp-tender, about 3 minutes. Transfer to a medium bowl.
In the skillet, heat the remaining oil over medium-high. Season the scallops and cook until golden, about 2 minutes. Turn; cook until just opaque in the center, about 1 minute. Divide among plates. Top with the romesco and serve with beans.
Bonus: We challenged dancer Misty Copeland to make this recipe! See how she did.