How to Make It
Stir together vinegar, sugar, red pepper flakes, 1 cup water and 1 tablespoon salt in a large saucepan; bring to a boil over high heat. Add ramps; reduce heat to medium-high and simmer for 5 minutes. Drain.
Process mayonnaise, Parmesan, garlic, 2 tablespoons water, 1 tablespoon of the lemon juice, 1 teaspoon black pepper and 1/2 teaspoon salt in a mini food processor until smooth.
Stir together 4 to 6 cups water (enough to cover artichokes) and remaining 1/4 cup lemon juice in a large bowl. Trim about 2 inches from top of each artichoke. Cut each artichoke in half vertically. Remove fuzzy thistle from bottom with a spoon; discard. Trim any leaves and dark green layer from base. Rub edges with lemon and place in lemon-water mixture. Once all artichokes are trimmed, remove 1 at a time from water and thinly slice with a mandoline or sharp knife. Place in a large bowl. Add dressing, arugula and mushrooms; toss to coat. Top with ramps.