Sauté shallots in 2 tablespoons of butter until translucent, add snow peas and sauté for another 5 minutes. Add the tomato halves, deglaze with the wine. Bring to the boil and stir in processed cheese. Season to taste with pepper and possibly salt.
Drizzle the fish fillets with lemon juice, season with salt and flour (knock off excess flour lightly). Fry on both sides in 2 tablespoon butter over low heat.
Arrange vegetables with fish fillets on plates. Serve sprinkled with dill.