For the Calabrian pepper aioli: In a food processor, combine and puree the lemon juice, Dijon mustard and peppers. Fold the mayonnaise into the puree and mix well. Reserve.
For the artichokes: Cut the artichokes in half lengthwise, splitting the stem. Remove the two bottom layers of leaves and, with a potato peeler, peel the stem until the outer fibers are removed. With a small spoon, dig out the inner fibers at the center of the artichoke.
Submerge the artichokes in a bowl of cold water and add the lemon juice to prevent browning.
Bring 1 gallon water to a boil and add 1/4 cup of the salt, stirring until dissolved. Add the artichoke halves to the boiling water and cook until a fork inserts easily into the stem, 10 to 15 minutes, depending upon the size of the artichoke. Remove from the boiling water and place in ice cold water to chill.
Heat a char broiler or wood-fired grill. Brush the cut side of the artichokes with the oil, season with the remaining 2 teaspoons salt and the pepper. Place cut-side down on the grill and cook until heated through.
Serve with the Calabrian pepper aioli.
Recipe courtesy of Shaun Brobak/ Brian Johnston, Crockett's Public House