How to Make It
Light a grill. On a sheet of foil, drizzle the garlic with 1 tablespoon of the olive oil. Season with salt and pepper and wrap tightly. Grill over moderately high heat, turning, until tender, 50 minutes. Unwrap and let cool.
Squeeze the garlic cloves into a mini food processor. Add the egg yolk, mustard, vinegar and lemon juice; pulse to blend. With the machine on, slowly drizzle in the remaining olive oil and the canola oil until incorporated. Season the aioli with cayenne, salt and pepper.
In a large cast-iron skillet set on the grill, cook half of the chorizo in 2 teaspoons of the olive oil over moderate heat until softened. Add half of the beans and cook until lightly charred and tender, 12 minutes. Stir in half of the shallots and cook until golden, 3 minutes. Season with salt and pepper. Transfer to a platter and repeat with the remaining ingredients. Serve the beans with the aioli and lemon wedges.