Step 1

Make the salsa verde: In a food processor, combine the parsley, oil, anchovies, garlic, water, lemon zest and juice, salt and crushed red pepper flakes, and process until smooth, stopping as needed to scrape down the sides with a flexible spatula. You should have about 2/3 cup.

Step 2

Make the sandwiches: Prepare the grill for direct heat (if using a grill pan, see Notes). If using a gas grill, set it to 450 degrees. If using a charcoal grill, fill a chimney starter with charcoal, light it, and when the coals are white-gray with ash, pour them onto charcoal grate, adding more charcoal, if necessary. Put the lid on the grill, making sure the vents are open all the way. When all of the coals are gray and hot, about 15 minutes, your grill should be medium-hot. (Use a grill thermometer, or test the heat by holding your hand, palm-down, about 4 inches from the grate, making sure that nothing flammable, such as clothing, is near the heat. If you can hold it there for about 4 seconds, the heat should be at medium, or about 450 degrees.) Pull your hand away from the heat before it gets painful.

Step 3

Lightly brush both sides of the fish and onion rounds with the oil and season one side with the salt and pepper.

Step 4

Place the fish and onion on the grill, and cook until grill marks form on the bottom, the onion softens and the fish is no longer translucent and flakes easily under the tines of a fork, 2 to 3 minutes per side for the onion and 3 to 4 minutes per side for the fish. Try not to move the fish too much, as it may fall apart.

Step 5

Toast the buns either on the grill or grill pan, or in a toaster.

Step 6

To assemble the sandwiches, spread about 1 tablespoon of the salsa verde onto the bottom side of each bun. Top each with a piece of fish. (If you prefer, trim the fish as needed to fit nicely in the bun.) Top with another 1 tablespoon of the salsa verde, then pile with the grilled onions, lettuce – gently crack on the ribs so the leaves lay flat – and the tops of the buns.