Cut off stems of artichokes; remove bottom leaves. Trim about 1/2 inch from tops of artichokes. Place artichokes, stem ends down, in a large Dutch oven filled two-thirds with water. Bring to a boil. Cover, reduce heat, and simmer 30 minutes or until a leaf near the center of each artichoke pulls out easily. Drain and rinse with cold water. Cool. Remove the bottom leaves and tough outer leaves, leaving tender hearts and bottoms; reserve leaves for another use. Cut artichokes in half lengthwise. Remove the fuzzy thistles from bottoms with a spoon. Coarsely chop artichoke hearts and bottoms. Place chopped artichokes in a large bowl.
While the artichokes are cooking, place potatoes in a saucepan, and cover with water; bring to a boil. Reduce heat, and simmer 15 minutes or until tender; drain and rinse with cold water. Cool. Cut potatoes into 1/4-inch-thick slices. Add potatoes and peas to chopped artichoke in bowl.
Cook mustard seeds in a small skillet over medium heat for 1 minute or until toasted. Combine mustard seeds, dressing, and remaining ingredients in a small bowl, and stir well with a whisk. Pour over the artichoke mixture, and toss well. Cover and chill.
Note: Substitute 1 cup of chopped drained canned artichoke hearts or bottoms for the fresh artichokes, if desired. If you are unable to find brown mustard seeds, substitute whole-grain mustard for the Dijon.