Slice off the bottom stems of artichokes along with the bottom few leaves. Cut off about 1/2 inch from the tops of the artichokes. Arrange artichokes, stem ends down in a large pot of Dutch oven filled 2/3 of the way with water. Boil on stove top. Lower heat, place lid on pot, and simmer 30 minutes or until artichokes are tender. Strain and run under cold water. Let cool.
Take off the bottom leaves and tough outer leaves of artichokes, leaving only the tender hearts and bottoms. Slice artichokes in half lengthwise and take out the fuzzy parts with a spoon. Roughly chop remaining artichoke pieces.
Cook potatoes in boiling water until tender, about 15 minutes. Strain and let cool. Slice potatoes into 1/4-inch thick pieces. Combine potatoes, peas, and chopped artichokes.
Toast mustard seeds for about 1 minute in a small frying pan. Whisk together mustard seeds, dressing, dill, lemon juice, mustard, salt, pepper, and garlic. Toss dressing with artichoke mixture. Place in refrigerator, covered until chilled.