Preheat your oven to broil and line a large, rimmed baking tray with aluminum foil. Brush foil lightly with 1 T oil to help the fish come off the pan easily.
While the oven is preheating, prep your other ingredients. Dice the tomatoes and slice the basil leaves thinly (julienne). Shred or grate the Parmesan if needed, and set aside.
Toss diced tomatoes and basil in a small bowl with remaining olive oil and season with salt and black pepper to taste. Set aside to marinate while fish cooks.
Arrange the haddock fillets on the prepared baking sheet and brush with 1 T of olive oil. Sprinkle with Parmesan cheese, and season each filet with a dash of salt and pepper.
Place in oven and broil for 6-8 minutes until the fish is golden-brown on top and flakes easily with a fork.
Remove from oven and set aside.
Spoon 1/4 of the tomato/basil onto a serving plate and nestle a filet of fish next to or on top.
Serve hot. Garnish with a wedge of lemon, if desired.