Bring to a boil 6 cups of water. Have ready a bowl of ice water. Add peas and 1 tablespoon of salt to the water and cook the peas for about 3 minutes, or until they are tender. Drain the peas and transfer them to the ice bath.
Bring another 6 cups of water to a boil. Add the potatoes and another tablespoon of salt and cook until just tender, 5 to 10 minutes. Drain the potatoes and let them cool off in a single layer in a cookie sheet so they will not overcook.
Whisk together the lemon juice and olive oil.
Combine the shallots and potatoes in a large bowl and toss with just enough of the lemon juice and olive oil to coat them well.
Rub the salmon all over with olive oil and season freely with the salt and pepper. Heat a large skillet with a shadow of olive oil over high heat. Add the fillets once hot and seat them without moving them for 4 minutes. Turn the fillets over and continue cooking until the salmon feels firm to the touch but still deep pink in the center. Another 3 to 4 minutes.
Just before serving, toss the peas and mint with the potatoes, adding a little more dressing to coat the peas well. Season with salt and pepper. Add the green salad and toss, adding a little bit more dressing if need be.
Spoon some salad into each plate and place the salmon on top of each salad. Drizzle with any remaining dressing. Serve with a wedge of salmon if you wish.