Lightly oil a large sheet pan. Finely slice the potatoes and trim the beans. Rub them lightly with olive oil. Season with salt and pepper. Chop 3 thin slices of lemon.
Place one salmon fillet, skin side down, on the chopping board. Season with salt, then lay the dill and parsley on top, followed by the lemon slices. Put the second fillet, skin side up, on top. Secure with a few pieces of cooking twine. Place in the middle of the baking sheet. Arrange the beans, potato slices and tomatoes around the fish. Squeeze lemon on the fish.
Cook for 15 to 20 minutes until the fish is cooked through. Turn the vegetables halfway through, if needed.
Mix together all of the salsa ingredients together.
Once cooked, allow the salmon to set for 5 minutes, then remove the twine and use a sharp knife to slice lengthwise through the salmon. Serve with the roasted vegetables and salsa.