If using favas, bring a large pot of water to a boil. Add favas and cook 2 minutes. Drain and rinse with cold water. Pull the top off tough skin on each bean and pop bean out of skin. Set beans aside.
Fill a large bowl with water and add juice from lemon. Working with 1 artichoke at a time, trim and discard stem end and about 2 in. of prickly top. Pull off and discard all tough outer leaves until only tender, very light green and yellow leaves remain (you may need to trim top further to fully remove leaves). Trim any tough green peel from stem. Be aggressive; you want the entire trimmed artichoke to be edible. Quarter artichoke lengthwise and scrape out the fuzzy choke (any choke left behind will add a lot of bitterness). Put trimmed artichoke in lemon water. Repeat with remaining artichokes.
Trim fennel bulb of dark and medium green tops. Chop feathery fronds and reserve 2 tbsp. of them. Discard remaining tops. Halve bulb lengthwise and cut into 1/4-in.-thick wedges. Set aside.
Trim root ends and dry or tough dark green leaves from green garlic and green onions. Cut into 2-in. pieces (if the green garlic has a small bulb on the end, halve it lengthwise). Set aside.
Heat olive oil in a large pot over medium-high heat. Add fennel wedges and drained artichokes. Sprinkle with 1/2 tsp. salt and stir until sizzling. Add green garlic, green onions, and 1 cup water; cover, reduce heat to medium, and cook, stirring occasionally, until artichokes are tender, about 20 minutes.
Add peas and fava beans, cover, and cook 2 minutes. Stir in fennel fronds and remove from heat. Add salt to taste.
Divide evenly among 4 shallow bowls and drizzle with extra-virgin olive oil.
Note: Nutritional analysis is per 1-cup serving.