In a medium pot, saute artichokes, onions, and carrots in olive oil for 5 minutes.
Add the dill, potatoes, lemon juice and 2 cups water. Simmer for 20 minutes. Add peas and simmer for 10 more minutes. Salt and pepper to taste.
When potatoes are done put corn starch in a bowl with a small amount of water (1/4 cup). Beat for 2 minutes and then add to the artichokes. Let it boil for 2 minutes.