Char the peppers over an open flame or under the broiler until blackened on all sides. Transfer to a plastic container with a lid or a paper or plastic bag. Cover the container or close the bag and let the peppers steam for about 15 minutes. Peel the skins from the peppers; then cut the peppers in half, remove the stems, and scrape out the seeds. Puree the peppers in a blender or food processor.
To make the mayonnaise, whisk the egg yolks and half the lemon juice together in a mixing bowl or blend in a food processor. Gradually beat in the olive oil until a thick emulsion is attained. Set aside
Add the pepper puree, garlic, and cayenne to the remaining mayonnaise. Season to taste with salt and add enough of the remaining lemon juice to bring up the red pepper flavor.