Preheat the oven to 450 degrees F (230 degrees C).
Heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the onion, garlic and carrot; cook and stir until onion is tender and transparent. Stir in the sugar, red pepper and mushrooms and continue to cook until onion is browned.
Sprinkle the flour over the vegetables and stir to blend. Cook for 1 minute then mix in the water and tomato paste. Season with basil and thyme. Mix in the beans and season with salt and pepper. Transfer to a greased casserole dish.
Pour the remaining oil into a shallow dish. Dip one side of each slice of bread in the oil, then arrange on top of the casserole with the oiled side up. Sprinkle Parmesan cheese over the top.
Bake for 10 to 15 minutes in the preheated oven, until the bread and cheese are toasted.
