Preheat the broiler to hot. Place the pepper under the broiler, skin-side up, until the skin has blackened. Peel off the skin and slice the flesh into strips.
Preheat the oven to 350°F
Place the olive oil in a 8in ovenproof frying pan over a medium heat. When the oil is hot, add the onion, bacon and potato and toss thoroughly. Reduce the heat to very low, cover and cook for about 15 minutes, stirring occasionally, until tender but not brown.
Lightly whisk the eggs and pour over the potato and onion mixture. Scatter over the red pepper, basil and cheese, then season with a little salt and a good grind of pepper.
Place in the preheated oven, uncovered, and cook for a further 12-15 minutes.
Using a palette knife, gently score around the cooked tortilla and lift the edges, then place a large plate face down over the pan and invert, turning the tortilla out onto the plate.
Cut the tortilla into portions and serve with a crisp salad, or by itself, drizzled with a little olive oil.