If using fresh bell peppers, preheat the broiler to high, with the top rack placed 6-8 inches from the heat source. Place the pepper on a small rimmed baking sheet (line the pan with foil for easier clean up).
Broil the peppers until the skin is blackened and they're soft and collapsed, turning frequently to roast evenly on all sides. You can also roast the peppers on an outdoor grill or right on top of a stovetop gas burner. Let the peppers cool until you can handle them, then peel off the skin and remove the stem and seeds.
Put the peeled, roasted peppers or drained jarred peppers in a food processor work bowl. Add the garlic, salt, vinegar, paprika and cayenne. Pulse until combined, then start pouring the oil in a steady stream while running the machine. Process until the sauce is smooth and creamy.
Taste for seasoning, adding more salt, cayenne or a touch of vinegar to adjust to your liking.
The recipe makes a little more than 1 cup of sauce, and doubles easily.
Romesco sauce keeps well up to a week, refrigerated. Bring to room temperature for best flavor before serving.
The peppers can be roasted up to 5 days ahead. Keep them in a covered container in the refrigerator, then proceed with step 3 of the recipe.