Step 1Heat the oven to 400 degrees. Halve the lemon lengthwise, then cut each half in half crosswise. Slice one of the lemon quarters very thinly crosswise. You'll need 5 or 6 slices per fish. Stuff the cavities of the fish with the lemon slices and a few parsley stems.
Step 2Place the salt in a large bowl and stir in 1 cup of water until the texture is that of gritty snow. Line a jellyroll pan with parchment paper and spread some of the salt in a layer about one-fourth-inch deep that is roughly the size of both fish. Place the fish on top of that, then mound the rest of the salt on top, covering them completely in a smooth, even layer. Roast the salt-encased fish in the oven for 20 minutes.
Step 3While the fish is cooking, put the parsley leaves on a cutting board with the half garlic clove and chop them together fairly fine. Place this in a bowl and add the olive oil. Whisk in 2 tablespoons lemon juice from the lemon and adjust seasoning for salt and lemon. The mixture should be savory and slightly tart.
Step 4After 20 minutes, remove the fish from the oven and let stand 5 more minutes to finish cooking. With a sturdy metal spoon or chef's knife, chip a crack around the base of the salt crust and carefully lift off the top. Use a dry pastry brush to brush away any salt on the surface of the fish.
Step 5Using a long spatula, carefully lift the fish onto the serving platter, turning it over in the process so you can brush away the salt on the underside. If you prefer, you can skin the fish -- the skin will be quite loose and come up easily.
Step 6Using a sharp knife, make a cut the length of the fish along the backbone. Carefully work the knife down the backbone until the fillet is freed. Make another cut right behind the head to free the fillet. Carefully lift the fillet to a warm serving platter, skin-side down, and remove any loose bones that are still attached.
Step 7Lift the tail of the fish, and the spine and ribs will come free. Cut behind the head again to free the second fillet. Transfer this fillet to the platter, skin-side down, and remove any loose bones. Spoon some of the sauce over the fillets and pass the rest at the table.