Place the egg yolks, garlic, cayenne and salt in the food processor. Puree until smooth, then add the red pepper and puree until smooth again.
While the mixture is pureeing slowly pour in the oil. Puree until the mixture has emulsified to your desired consistency. Taste, then salt as needed. Cover and refrigerate until ready to serve.
Fill a large pot with 2 inches of water and place a steaming basket over it. Cover and bring to a boil.
Trim the artichoke stems off, and trim 3/4 inch off the top of the artichoke flower. Pull off any damaged leaves around the base. Using kitchen shears, trim each point off the outer leaves. Squeeze lemon juice over the cut edges to reduce browning.
Sprinkle with salt and place in the steam basket. Cover and steam the artichokes for 30-40 minutes, until a center leaf pulls out easily.
Serve the artichokes with the aioli on the side for dipping!