In a large skillet heat 1 Tbsp of olive oil over medium high heat. Add the onions, red pepper, eggplant and cherry tomatoes and cook covered with a lid for about 10 - 13 minutes until the vegetables are tender, stirring frequently. Season the vegetable mixture with salt and pepper.
Add the garlic, capers, olives, tomato puree, tomato paste, coconut sugar (or honey/maple syrup), balsamic vinegar, salt, pepper and red pepper flakes (optional), and cook for 2-3 more minute. Check for seasoning and adjust to your own liking.
Season fish with lemon juice, salt, and pepper on both sides and place on top of the eggplant caponata in the skillet. Cover with a lid and cook for about 10 minutes over medium high heat.
The sauce should be thick and have reduced by half.
Plate the fish on a plate and pour some of the eggplant caponata sauce on top. Sprinkle with fresh basil.