Preheat over to 450 degrees.
Cut the ends off the garlic cloves and roast in a garlic roaster or wrapped in aluminum foil in the oven for 20-30 minutes, until tender. Squeeze out roasted garlic into a small bowl. Add mayonnaise and lemon juice to the bowl and stir to combine, making sure to mash up the garlic well. Season with salt and pepper to taste. Set the aioli aside.
In a large bowl, toss broccoli florets with olive oil, 1 Tbsp lemon juice, and red pepper flakes. Spread in an even layer on a baking sheet. Season with salt and pepper.
Roast the broccoli for 10 minutes. Sprinkle the cheese over the broccoli and roast for an additional 5 to 10 minutes. Drizzle garlic aioli over the broccoli. Serve warm.