Trim off the top of each head of garlic and remove any loose outer skin.
Place garlic heads on a piece of foil, cut-side up.
Drizzle with the oil and season with salt and pepper.
Wrap heads up in foil and bake 50-60 minutes or until the garlic is soft.
Remove, unwrap and let cool.
Squeeze the heads to remove the garlic cloves. Mash with the back of a knife.
In a small mixing bowl, whisk together the mayonnaise, lemon juice, Worcestershire sauce, cayenne pepper and mashed roasted garlic.
Refrigerate for 12-24 hours.
For the radishes
Heat 2-3" of oil to 375 F in a deep-fryer or Dutch oven.
In a large bowl, whisk together the beer, all-purpose flour, garlic powder, salt, pepper and parsley flakes until a batter forms. You may have to add more beer if it's too thick but don't add too much! Just a little at a time. If the batter gets too thin add a little flour and whisk.
Add in the sliced radishes and toss to coat.
Working in batches, deep fry the radishes until golden brown.
Remove to a paper towel-lined plate or baking sheet with a wire rack to drain.
Serve with the garlic aioli for dipping.
Notes
Make the garlic aioli the day ahead.You might have leftover aioli. It's great on hamburgers!Depending on the size of the radishes and how thick or thin you cut them, you might have extra batter. Just deep-fry more of them!