Heat the oven to 250 degrees. Pour 1/4 cup olive oil into a parchment pouch just large enough to hold the salmon in one piece. Lay the salmon, skin side down, in the olive oil. Sprinkle generously with sea salt and pepper.
In a food chopper or food processor, blend the shallot, dill, parsley and lemon zest. Blend in the remaining 2 tbsp. olive oil. Pat herb paste on the salmon. Bake for 22 to 28 minutes, depending on the thickness of the fillet. To check for doneness, insert the tines of a fork into the thickest part of the fillet and gently pull apart. If the fish flakes easily, then it is done.
To serve the salmon, gently slide a spatula under the fish and transfer to a cutting board. Use a sharp knife to cut the fillet into four equal pieces. If desired, lift the fish away from the skin to serve.