How to Make It
Set a large perforated grill pan to one side of a grill's cooking grate. Heat grill to medium-high (450°).
In a large bowl, whisk together parsley, mint, lemon juice and zest, allspice, 2/3 cup olive oil, and 1/4 tsp. salt. Reserve 1/2 cup herb oil and set aside. Whisk 1/4 tsp. salt and the pepper into herb oil in bowl; add chicken and turn to coat well.
Set chicken next to grill pan and grill, covered, 5 minutes. Discard marinade.
Gently toss tomatoes with remaining 2 tbsp. olive oil, plus salt and pepper to taste. Arrange tomatoes in a single layer on grill pan. Turn chicken over. Cook tomatoes and chicken, covered, until tomatoes are softened with a bit of char and chicken is nicely browned and cooked through (cut to test), 4 to 6 minutes.
Transfer tomatoes to a platter. Arrange chicken on top and drizzle with 1/4 cup reserved herb oil. Serve with remaining herb oil.