Peel the red onions and cut them into thick slices. Leave the garlic cloves whole. Halve the jalapeno pepper and remove the seeds if you prefer a milder flavor.
Brush the onion, garlic, and jalapeno pepper with a little olive oil, then sprinkle with smoked paprika, salt, and pepper.
Preheat the grill to medium-high heat, then place the vegetables on it. Grill for 5-7 minutes, until the red onion is caramelized, the garlic is softened, and the jalapeno is slightly charred.
Remove the vegetables from the grill and let them cool slightly. Squeeze the garlic out of its skin and place it in a food processor with the red onion and jalapeno pepper.
Add the BBQ sauce, balsamic vinegar, and chili flakes, and purée until smooth and creamy.
Taste and, if necessary, season with more salt, pepper, or extra smoked paprika.
Sprinkle with fresh parsley and serve as a sauce with roasted meats, grilled vegetables, or toast.
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