Remove fish from the refrigerator 20 minutes before cooking, and sprinkle a little salt on both sides. Pat fillets dry; damp or moist fillets are much more likely to stick to the pan. Dust fillets with flour and shake off any excess. Sprinkle both sides with salt and pepper.
In a steel pan, add 1 tablespoon oil and 1 tablespoon butter. Heat on medium high until butter is melted but not browned, then reduce heat to medium.
Place fillets in the pan. Don’t touch fillets until ready to flip. After about 3 minutes, try to slide the spatula under the fish. If the fish releases easily from the pan, flip it; if not, try again in a few seconds. It will release when the bottom of the fish is done cooking.
After flipping, divide remaining 1 tablespoon of butter over both fillets and cook fish for another 2–3 minutes, or until done. Fish will be golden on both the top and bottom and opaque all the way through when finished cooking.
Transfer the fish to plates, leaving the excess butter in the pan. Cover fish to keep warm, or set fish in a 200ºF oven.
Add remaining oil, onion, and garlic to the pan and cook until shallots are translucent, 2–3 minutes. Add wine and deglaze the pan with a wooden spoon. Add capers, cherry tomatoes, and lemon zest. Cook for about 5 minutes, stirring occasionally, until tomatoes are blistered.
Serve fish hot with the pan sauce.
Note: Fish can be served over a bed of mashed or roasted potatoes.