1. Cut the salmon in pieces, and trim off any very thin edges to get two equal pieces of relatively even thickness. Season with salt and pepper and set aside.
2. Melt one and a half tablespoons of the butter in a skillet over medium heat. Add the shallots and cook, stirring frequently until they are translucent and softened, three to four minutes. Add the peas and season with salt and pepper. Let them cook, stirring occasionally, until the peas are cooked through. Lower the heat, and let them sit until you need them again.
3. Meanwhile, heat the chicken stock and the juice from half a lemon over low heat until hot, stir in the remaining half tablespoon of butter, cover and keep warm until ready to serve.
4. Heat the olive oil and another tablespoon of butter in a skillet over medium high heat until hot. Add the salmon to the skillet skin side up and let it cook, without disturbing it for four minutes or so, until the fish is well browned. A good tip to remember, the fish will be easily flipped without sticking when the fish is well browned. If the fish sticks, let it cook for another minute until it releases easily. Cook the fish, skin side down for another three to four minutes, until the skin is crispy and browned and the filets are cooked through. Remove from the pan and let the fish rest.
5. Put the hot peas in a blender or food processor, and process until pureed and mashed, but still chunky. Put half the peas on each plate, top with the salmon and spoon half the broth over and around the fish and peas. Serve immediately.