Poached Salmon with Artichoke Confit

Add 3 tablespoon lemon juice to a large bowl of cold water. Working with 1 artichoke at a time, remove tough dark outer leaves. Using a serrated knife, trim top of artichoke to just above the heart. Trim stem, leaving about 1" intact. Using a paring knife or vegetable peeler, remove dark outer layer from stem. Halve artichoke lengthwise and scoop out choke with a spoon. Transfer artichoke to lemon water to prevent discoloration.
Drain artichokes; pat dry. Cook with thyme, garlic, bay leaves, peppercorns, and oil in a large saucepan over medium heat until oil around artichokes is bubbling. Reduce heat and cook, turning artichokes occasionally, until stems are tender when pierced with a knife, 15-20 minutes; let cool in oil.
Meanwhile, if using fresh fava beans, cook in a medium saucepan of boiling salted water until tender, about 4 minutes. Using a slotted spoon, transfer to a colander set in a bowl of ice water. Drain and peel; place in a large bowl. (If using frozen fava beans, cook 2 minutes; do not peel.)
Return water in saucepan to a boil; add peas and cook until tender, about 2 minutes. Drain; transfer to colander in ice water. Drain and add to bowl with fava beans.
Using a slotted spoon, transfer artichokes to bowl with peas and fava beans. Add 1/4 cup artichoke cooking oil, olives, pea shoots, mint, and remaining 2 tablespoon lemon juice; toss and season with salt and pepper.
Do Ahead: Artichokes can be poached 1 day ahead. Keep in oil; cover and chill.
Bring parsley, dill, lemon slices, lemon juice, wine, peppercorns, and 3 cups water to a simmer in a large saucepan over medium heat; season with salt. Add salmon; cover. Reduce heat and simmer gently until just opaque throughout, 6-8 minutes. Using a large spatula, remove salmon and lemon slices from poaching liquid. Serve salmon with artichoke salad and lemon slices.