Prep the fish and mise en place: pat the fillets dry with paper towels and cut into 1½–2 cm thick portions if needed so they cook evenly. Season both sides lightly with salt and cracked black pepper. Patting the fish dry removes surface moisture so it browns lightly and the sauce won’t become diluted.

Heat a large, heavy skillet or shallow Dutch oven over medium-high heat. Add 2 tsp of olive oil and the butter. When the butter begins to foam and the fat is shimmering (about 1 minute), add the polenta cakes in a single layer. Sear without moving for 2–3 minutes until the underside is deep golden and crisp — a hot pan creates Maillard browning that gives the polenta a nutty, crunchy contrast to the soft fish.

Flip the polenta cakes and crisp the other side for 1–2 minutes. Transfer the cakes to a plate and tent loosely with foil to keep warm. Using the same pan means the fond (browned bits) will flavor the sauce — that’s deliberate.

Lower the heat to medium. Add the remaining 2 tsp olive oil to the pan. Add the diced onion and a pinch of salt; cook, stirring occasionally, until translucent and beginning to brown around the edges (about 4–5 minutes). Browning the onion builds savory depth in the tomato braise.

Add the minced garlic and cook for 30–45 seconds until fragrant. Be careful not to burn the garlic — brief cooking releases its aroma and sweetens the flavor without becoming bitter.

Pour in the canned diced tomatoes with their juices. Use a wooden spoon to scrape up any browned bits from the bottom of the pan (deglazing) — those bits add concentrated flavor. Bring the tomatoes to a gentle simmer and reduce the heat to maintain a low simmer for 6–8 minutes so the sauce thickens slightly and the flavors concentrate.

Stir in the halved Kalamata olives and capers. Taste the sauce before adding more salt: olives and capers are salty, so you may not need much extra. Add freshly cracked black pepper and 1 tbsp lemon juice if using to brighten the sauce.

Nestle the seasoned fish pieces into the tomato mixture in a single layer, spooning a little sauce over the top of each piece. Cover the pan and simmer gently for 6–8 minutes (depending on thickness) until the fish is opaque and flakes easily with a fork. A gentle covered simmer ensures the fish cooks through without drying — rapid boiling will toughen delicate white fish.

Once the fish is just cooked, return the polenta cakes to the pan, tucking them partially into the sauce so they absorb some flavor and reheat (about 1–2 minutes). This step integrates the textures while keeping the polenta’s crisp edges from going completely soggy.

Remove the pan from the heat. Sprinkle the chopped basil and parsley over the fish and drizzle with the remaining teaspoon of olive oil. Let the dish rest for 1 minute; the residual heat will settle the sauce and brighten the herbs. Adjust seasoning with salt and pepper if needed (remember capers/olives add salt).

To serve: place 2 polenta cakes on each plate and top with a piece or two of the braised fish and spoonfuls of tomato, olive and caper sauce. Finish with an extra grind of black pepper and an optional lemon wedge for squeezing at the table.