In a medium bowl, combine tomatoes, onion, capers, olive oil, basil, lemon juice, shallots, 1 teaspoon salt, and 1/2 teaspoon black pepper, stirring gently. Cover and refrigerate to allow flavors to meld, preferably at least an hour or up to 1 day.
When ready to finish the recipe, position oven rack about 5 inches from broiler, and preheat broiler.
Meanwhile, place fish fillets on a rimmed baking sheet. Season both sides of the fish evenly with the remaining 1/8 teaspoon salt and 1/16 teaspoon pepper.
Broil fish on first side for about 4 minutes. (I prefer to put the side that used to have the skin upwards for this first broiling step, just so you finish the recipe with the more attractive side up and the skin-side down.)
Remove the fish from the oven, flip the fish over, and top the fish evenly with the tomato topping mixture.
Continue broiling until the fish is done (about 8 minutes depending on your broiler and the exact thickness of your fish.) The fish should be opaque and flake easily with a fork in the thickest part of the fillet.
Serve immediately, with lemon wedges, if desired.
Choosing your fish: As noted in the post above, we recommend a mild white fish for this recipe. At The Fish House, options include mahi mahi, grouper and snapper. At home, we tested the recipe using inexpensive and readily available cod, which was also delicious.
Make-ahead steps: Because the tomato topping is best if made ahead and refrigerated for at least an hour (or up to a day ahead), almost all of the work in this recipe can be completed ahead of time.
Gluten-free note: This recipe is gluten free, as long as the vinegar in the jarred capers you use is gluten free. Most vinegars are gluten free, but if you have any doubts, look for a jar of capers that's specifically denoted as being gluten free. (If you're interested, here's a great post on What Vinegars Are Gluten-Free.)