Roast the hazelnuts in a pan without oil, stirring constantly. Set aside.

Heat the broiler.

Arrange an oven rack in the position closest to the flame. Place the peppers (cut side down), the tomato halves (cut-side uand the garlic on a rimmed baking sheet. Broil until the peppers and the garlic are slightly charred, 3 to 5 minutes.

Turn the garlic (but do not turn peppers or tomato); broil 1 to 2 minutes longer until the garlic is well browned but not burned. Transfer the garlic to a large bowl.

Continue broiling the peppers and the tomatoes until both are well charred, 4 to 5 minutes longer. Transfer the tomato and the peppers to the bowl with the garlic.

Cover the bowl with plastic wrap. Let it stand until the vegetables are cool enough to handle but still warm, then peel the peppers and the tomatoes.

In the bowl of a food processor fitted with the blade attachment, pulse the hazelnuts until they are coarsely ground. Add the peppers, tomato, garlic, breadcrumbs, oil, vinegar, honey, paprika, salt and purée until it is smooth. Taste and adjust the seasonings. Scrape the romesco into a bowl.

Bring a large pot of salted water to a boil. Have ready a large bowl of ice water. Boil the broccoli until just tender, 2 to 3 minutes. Use a slotted spoon to transfer them to the ice water; drain.

In a large bowl, toss the broccoli with enough romesco to coat the vegetables well. (Reserve any remaining romesco for dipping or for another use.) Garnish with the hazelnuts and serve warm or at room temperature.