In a food processor, combine the artichokes, marinated mushrooms, shallot, tarragon, and vinegar. Season with salt and pepper and turn processor on and stream in about 1/2 cup of evoo until a spoonable, fairly smooth dip forms, about 1 minute. Scrape the dip into a serving bowl and place a demitasse (small) spoon in the dip so it can be easy applied to each individual cooked lamb chop.
Drizzle chops with a few teaspoons of evoo and season with salt and pepper. Grill or broil 2 minutes on each side and remove to rest.
To serve, place dip on large platter or cutting board and surround with cooked chops and piles of baby cut carrots, sugar snap peas and halved radishes for dipping and topping. Garnish platter with additional sprigs of tarragon.