Heat olive oil in a large deep skillet. Add the leeks, celery, onion and carrot and cook over low heat, stirring often, until softened but not browned, about 20 minutes. Add the garlic and cook until fragrant, about 1 minute.
Add the frozen artichokes, sliced fennel bulb, lemon juice, thyme, tarragon and bay leaves; season with salt and pepper. Add the wine and broth, cover partially and braise over moderately low heat until tender, about 15-20 minutes. Stir in peas and cook 2 more minutes. Discard the herbs.
Meanwhile, blanch the asparagus and beans separately in boiling salted water until crisp tender, about 3-4 minutes. Transfer vegetables to a bowl of ice water to stop cooking and retain bright colors.
Mound the asparagus and beans in soup plates and spoon braised artichokes and fennel on top. Scatter chopped tomatoes and fresh herbs on top.
Adapted from Tom Colicchio’s recipe as seen in Food & Wine, June 1999. To lighten the dish, I reduced the amount of olive oil. To simplify the recipe, I used frozen artichoke hearts. I also decided to braise the fennel along with the artichokes.