Halibut with Raw Puttanesca Salsa

4 (6-ounce) halibut fillets

Extra-virgin olive oil, for liberal drizzling plus 1/4 cup

Salt and freshly ground black pepper

4 (1-inch) thick slices crusty bread

1 1/2 teaspoons anchovy paste

2 to 3 cloves garlic, grated

1 teaspoon crushed red pepper flakes

1 lemon, zested and juiced

3 tablespoons capers, run your knife through them

1/2 cup pitted black olives, chopped

1/2 cup flat-leaf parsley, coarsely chopped

1 pint grape tomatoes, halved or cherry tomatoes, quartered