01 - Preheat oven to 400°F.
02 - Slice the top off the garlic bulb to expose the cloves. Drizzle with 1 tablespoon of the olive oil, wrap tightly in aluminum foil, and roast for 20 minutes until the cloves are soft and fragrant.
03 - Allow the garlic to cool until comfortable to handle, then squeeze the roasted cloves from their skins into a small bowl.
04 - Using a fork, mash the roasted garlic thoroughly until a smooth paste forms.
05 - In a mixing bowl, whisk together the mayonnaise, remaining 1 tablespoon of olive oil, smoked paprika, lemon juice, liquid smoke, salt, and pepper until evenly blended.
06 - Fold the roasted garlic mash into the mayonnaise mixture, stirring until fully incorporated and no large clumps remain.
07 - Taste the sauce and adjust salt, pepper, or liquid smoke to achieve the desired level of smokiness and seasoning.
08 - Transfer to a serving bowl and serve chilled or at room temperature as a dip, spread, or accompaniment to grilled dishes.