Preheat oven to 400F. Slice off about 1/2 inch of the top of 2 full heads of garlic. Drizzle olive oil over the top of the heads of garlic and season with salt and pepper. Wrap the heads of garlic in tinfoil and place in a baking dish.
Roast the heads of garlic in the oven at 400F for 40 minutes. Remove the garlic from the oven and carefully open the tinfoil. Allow the roasted garlic heads to cool until you can hold them without them being too hot.
Add the mayonnaise, lemon juice, dijon mustard, smoked paprika, and balsamic vinegar to a food processor. Squeeze the roasted garlic cloves out of the heads of garlic and into the food processor.
Turn on the food processor and process until a smooth and even mixture remains. Transfer to a glass storage container and store in the refrigerator.