Preheat an oven to 350 degrees F (175 degrees C).
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Cook onion and red pepper in the oil until onion is tender and golden, and peppers are slightly soft, about 10 minutes. Stir balsamic vinegar into the vegetables; season with salt and pepper.
Rub tilapia filets with 2 teaspoons olive oil and a sprinkle of salt and pepper. Place fillets in a small baking dish, and top with the balsamic onion mixture. Sprinkle fish evenly with blue cheese.
Bake in preheated oven until fish flakes easily. Serve atop salad greens.