Heat the broiler. Arrange an oven rack in the position closest to flame. Place peppers (cut side down), tomato halves (cut-side up) and garlic on a rimmed baking sheet. Broil until peppers and garlic are slightly charred, 3 to 5 minutes. Turn garlic (but do not turn peppers or tomato); broil 1 to 2 minutes longer until garlic is well browned but not burned. Transfer garlic to a large bowl. Continue broiling peppers and tomatoes until both are well charred, 4 to 5 minutes longer. Transfer tomato and peppers to the bowl with the garlic. Cover bowl with plastic wrap. Let stand until vegetables are cool enough to handle but still warm, then peel peppers and tomatoes.
In the bowl of a food processor fitted with the blade attachment, pulse hazelnuts until coarsely ground. Add peppers, tomato, garlic, breadcrumbs, oil, vinegar, pomegranate molasses, paprika and salt. Purée until smooth. Taste and adjust seasonings. Scrape romesco into a bowl.
Bring a large pot of salted water to a boil. Have ready a large bowl of ice water. Boil broccoli until just tender, 2 to 3 minutes. Use a slotted spoon to transfer to ice water; drain.
In a large bowl, toss broccoli with enough romesco to coat vegetables well. (Reserve any remaining romesco for dipping or for another use.) Garnish with hazelnuts and serve warm or at room temperature.
** This recipe came from a New York Times recipe column by Melissa Clark. When we read through it, we had recently been to Jaleo and had their roasted asparagus over Romesco and decided we wanted to make it at home. This column gave us the lead we needed; we substituted roasted asparagus for the broccoli and toasted almonds for the hazelnuts and then used our approach to roasting the red peppers and tomatoes.