Step 1

Using a small food processor, pulse the anchovies and garlic into a paste. Add the lemon juice, mustard and honey and process until smooth. With the processor running, slowly stream in the grapeseed or canola oil and the olive oil. Stop the machine and, using a leaf of romaine, taste the dressing, adding salt, pepper and more lemon juice as needed, pulsing for another second or two to combine. (This may also be done by hand: On a cutting board, using a chef’s knife, chop and crush the anchovies and garlic into a paste. Add them to a medium bowl and whisk in the lemon juice, mustard and honey. Whisk the oils into the dressing in a steady stream until it’s emulsified and thick. Season to taste with salt and pepper.)

Step 2

Heat the grill to about 350 degrees. If using a grill pan, it should be very hot but not smoking (see headnote). If grilling over charcoal, use a grill thermometer or use the hand method: If you can hold your hand an inch from the grill for about six seconds, the grill should be around 350 degrees.

Step 3

Spread 1 generous tablespoon of dressing over each salmon filet. Using a pastry brush, spread some dressing on both sides of each slice of bread. Very lightly brush the cut side of each romaine head with dressing, and season each one with a small pinch of salt and a few grinds of pepper. Very lightly brush the asparagus and the cut side of each lemon half with oil.

Step 4

Grill the romaine heads, cut side down, until lightly burnished, 1 to 2 minutes. Flip and grill for 1 more minute; the romaine should be charred but not limp. Using tongs, remove them from the grill and place onto a serving platter.

Step 5

Using tongs, place the asparagus in a single, tight row perpendicular to the grill grates. Lay the salmon, skin side down, atop the asparagus. Place the bread and lemon halves, cut side down, near the cooler edges of the grill. Close the grill (or cover the grill pan) and cook, checking once to be sure the grill isn’t overheating, for 4 to 5 minutes, until the bread is lightly charred on one side.

Step 6

Flip the bread, rotate the lemon halves, and then cover and cook for another 4 to 6 minutes, or until the fish has reached an internal temperature of at least 120 degrees, and the asparagus, bread and lemons are lightly charred.

Step 7

Using tongs, layer the salmon, asparagus, lemons and grilled bread on the serving platter with the grilled romaine. Stir the Parmesan into the remainder of the dressing and drizzle some on the romaine, top with more grated cheese, if desired, and serve, with extra dressing on the side.