Rinse the courgette, halve it lengthwise, and cut into equal half-moons. Finely chop the garlic and season the cod fillet with salt and pepper. Make a quick pesto by finely pounding the fresh basil, pine nuts, and one tablespoon of the olive oil in a mortar, or briefly puree with a food processor.
Heat the remaining tablespoon of olive oil in a large frying pan over medium-high heat. Add the courgette half-moons and finely chopped garlic. Fry this, stirring regularly, for approximately five minutes until golden brown and cooked through. Remove the vegetables from the pan and set aside on a plate.
Place the seasoned cod fillet in the remaining cooking fat in the same frying pan. Fry the fish on both sides for approximately two to three minutes until golden brown, until the inside is just cooked and the fish flakes separate easily.
Divide the warm courgette over the center of a plate and carefully place the fried cod fillet on top. Spoon the homemade basil pesto over the warm fish, add a pinch of salt or pepper to taste if needed, and serve immediately.