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.
Notes
You can either use store bought mayo or make your own. With my one minute mayo, making mayo at home is easy! You blend egg and oil until the egg yolks go through emulsion, which means they've thickened and fully combined. Then I just add a little lemon and some spices.
Instead of the balsamic vinegar, you could try worcestershire sauce. It will be a little less tangy and add a bit of umami.
You can make so many variations of this aioli. To spice it up, you could add some cayenne pepper, or you could even whisk in a dash of sriracha. For an herby aioli, you could add something like rosemary or basil.