Preheat the oven to 190°C (Gas Mark 5 / 375°F).
Heat the oil in a large frying pan, and add the onion, mushrooms, peppers, and garlic. Cook over a medium heat for 5 minutes, stirring regularly, until the vegetables are soft.
Remove the vegetables from the heat, and add the basil pesto and a pinch of salt and pepper. Mix well.
Spoon a quarter of the vegetable mixture along the centre of one of the large flour tortillas, and tightly roll. Place the tortilla seam side down in a baking dish, and repeat with the remaining vegetables and tortillas.
Pour the pizza sauce over the enchiladas, and top with the grated cheese. Top with a few extra slices of mushroom.
Bake for around 30 minutes, or until the cheese topping is crispy and golden brown. Serve topped with fresh basil if desired.