Preheat oven to 350ºF.Arrange hazelnuts and bread on a rimmed baking sheet. Bake for 8 to 10 minutes, shaking the pan once halfway through, until toasted.
Prepare Romesco:To the bowl of a food processor, add hazelnuts. Pulse a few times until they are finely chopped. Next, add bread, roasted red peppers, tomato paste, vinegar, garlic, smoked paprika, salt, and pepper.With motor running, gradually stream in olive oil, blending until the sauce is mostly smooth.
Prepare Broccoli:Heat 2 Tbsp. olive oil in a large skillet (preferably a cast iron) over medium-high. Once hot, arrange baby broccoli in pan and cook, undisturbed, for 2 to 3 minutes. Toss, and continue cooking for 5 to 6 more minutes, stirring only occasionally, until the stalks are lightly charred and stems are tender.During the final minute, add half of the butter. Once melted, toss with broccoli. Season with salt and pepper, and transfer broccoli to a plate. Reduce heat to medium.Add remaining half of butter. Once melted, arrange lemon slices over butter, and cook, undisturbed, for 2 to 3 minutes, or until the lemons are caramelized.
Arrange broccoli on a platter. Spoon hazelnut romesco overtop (you only need about half the batch), and garnish with caramelized lemon. If desired, sprinkle the dish with fresh chopped parsley and a few grinds of black pepper.
