Step 1

Prepare a grill for medium-high heat. Cut lemon in half crosswise and thinly slice 1 half; remove seeds. Set remaining lemon half aside for serving. Grill lemon slices, turning occasionally, until lightly charred, about 2 minutes. Transfer to a cutting board and coarsely chop. Place in a medium bowl.

Step 2

Using long tongs, place clams directly on grill. Carefully transfer to a large bowl as they open. (Try to save as much clam liquor as possible, but some will inevitably spill onto coals.) Let cool.

Step 3

Remove clams from their shells and coarsely chop. Transfer clams and any liquor to bowl with lemon and add garlic, parsley, red pepper flakes, and ¼ cup oil; season with salt and black pepper.

Step 4

Drizzle bread with oil and grill, turning halfway through, until toasted and lightly charred, about 5 minutes.

Step 5

Top toasts with clam mixture, some Green Olive Tapenade, then Parmesan, dividing evenly; cut into pieces. Cut reserved lemon into wedges and serve alongside toast for squeezing over.