Juice from one Meyer lemon (or regular lemon juice, which is tarter, to taste)
1 cup olive oil
1 large egg yolk
2 cloves garlic
½ teaspoon dijon mustard
½ teaspoon red pepper flakes
salt and pepper, to taste
Clip the leaves of the artichokes to remove the thorn at the tips, and slice off the top ¾ of an inch. Bring a pot of generously salted water to a boil and add the artichokes. Boil for about 25 minutes, or until the outer leaves can be easily pulled off. Take out the artichokes, submerge in ice-cold water until cool, and then drain.
Heat the grill. Charcoal is the best choice because the smoke adds additional flavor. But, if you must, a gas grill will do.
Cut the artichokes in half and pull out the thistle heart (purple and white leaves in the middle). Using a pastry brush, coat the artichokes with olive oil inside and out. Salt and pepper all over and place them cut side down on the cool side of a hot grill. Because the olive oil will attract flames and burn them, keep them away from hot coals.
Turn often until some of the outer leaves begin to crinkle and darken. Remove to a platter and allow to cool. Serve with aioli.
Add the lemon juice, egg yolk, garlic, mustard and red pepper flakes to the pitcher of a blender or food processor and put the top on. Turn on blender/food processor and remove the safety top.
Slowly pour in about half of the olive oil until the mixture is emulsified.
Turn off the blender and add a pinch or two of salt and one of pepper, or to taste.
Restart the blender and add the remaining olive oil, or enough to make the sauce thick and creamy. Pour into dipping bowls.