Cut off the top of the garlic head, exposing the cloves slightly. Drizzle with a little oil, then wrap in aluminum foil.
Preheat your grill to medium heat, then place the wrapped garlic on the grill. Cook for 20-25 minutes, or until the cloves are completely softened and slightly caramelized.
Remove the garlic from the grill and let it cool. Squeeze the soft, roasted garlic cloves into a small bowl and mash into a paste.
In a bowl, whisk together the egg yolks, mustard, and lemon juice.
While continuously whisking, slowly drizzle in the sunflower oil until you achieve a thick, creamy mayonnaise.
Add the BBQ sauce, smoked paprika, salt, pepper, and mashed roasted garlic to the mayonnaise and mix thoroughly.
Refrigerate for at least 30 minutes to allow the flavors to meld.
Serve as a dip with fries, grilled meats, or sandwiches.
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