Arrange the sliced tomatoes on a large platter and set
aside. Pat the skin of the halibut dry with a paper towel and then brush
the fillets all over with olive oil. Season the flesh generously with
salt and pepper.
Oil the grill grates and put the cherry tomatoes and fish
skin-side down on the grill. Cover and let cook until the tomatoes are
charred and starting to split, about 5 minutes, depending on the
ripeness of the tomatoes and the heat from your grill. Cook the halibut
until just cooked through, about 10 minutes. Transfer the fish skin-side
down to the platter with the sliced tomatoes.
Put the cherry tomatoes in a blender, discarding the vine,
and add the olive oil, vinegar, 1 teaspoon salt and several grinds of
pepper. Blend until smooth, then stir in half the chives and basil.
Spoon the tomato vinaigrette over the fish and tomatoes. Drizzle
everything with some more olive oil and sprinkle with the remaining
chives and basil. Finish with a sprinkle of flaky salt.