While the grill heats, prepare all components for assembly. Grill the lemons first (they take the longest) by cutting them in half crosswise and setting them aside. Make the dressing by blending the anchovy fillets, peeled garlic clove, Dijon mustard, 1/4 cup lemon juice (from the grilled lemons once cooled), and 3/4 teaspoon freshly ground black pepper in a blender for 20 seconds until smooth. Add 1/4 cup extra-virgin olive oil and blend for 10 more seconds until emulsified. Transfer to a bowl and stir in the finely grated Parmigiano-Reggiano. Set the dressing aside. I find making the dressing ahead keeps the final assembly quick and lets the flavors meld slightly.

Preheat your grill to 400°F. Pat the 24 oz salmon fillets dry with paper towels, then coat the flesh side with 1 teaspoon olive oil, 3/4 teaspoon kosher salt, 1/2 teaspoon freshly ground black pepper, and 1/4 teaspoon red pepper flakes—this creates a flavorful crust when grilled. Brush the cut sides of the 4 romaine hearts with olive oil and season with salt. Cut the 4 oz sourdough bread into 1-inch thick slices and brush both sides with olive oil and a pinch of salt. Have all items ready to grill in order of cooking time.

Place the lemon halves cut-side down on the grill for 6–8 minutes until they develop golden char marks and release their juice. This caramelization adds depth to the dressing and provides a garnish. Set them aside to cool slightly.

Place the sourdough slices on the grill for 3–5 minutes per side until golden and crispy with grill marks. Remove and cut into 1-inch pieces. Next, grill the romaine heart halves cut-side down for 3 minutes, then flip and grill for 3 minutes more until they have light char and begin to soften slightly. The heat wilts the outer leaves while keeping the hearts crisp. Transfer all to a cutting board.

Place the seasoned salmon fillets skin-side up on the grill for 3 minutes. Flip carefully and grill skin-side down for another 3 minutes until the internal temperature reaches 125°F to 145°F (depending on your preference for medium-rare to medium). The skin will crisp beautifully and help keep the fish moist. I prefer to let the salmon rest for 2 minutes off the grill before cutting to keep it from drying out.

Arrange the grilled romaine halves on serving plates. Break the grilled salmon into large chunks and place on top of the romaine. Add the grilled bread pieces around the salad. Drizzle the Caesar dressing from Step 1 generously over the salad and garnish with the charred grilled lemon halves on the side for squeezing. Serve immediately while everything is still warm.