Heat 2 tbsp olive oil in a 20cm cast iron frypan over low/ med heat. Add the onions and cook until caramelised, about 15 minutes. Set aside.
Heat the remaining oil in the frypan over med/ high heat and fry the potatoes until golden and tender.
Preheat oven to 180C. Place the potatoes, onions and eggs in a medium bowl, season with salt and pepper and gently stir to combine, leaving the yolks and whites separate and streaky.
Leave 2 tbsp olive oil in the cast iron pan, heat over medium heat and pour in the tortilla mixture. Cook for 2 minutes, then transfer into the oven and cook until just set, about 8 minutes.
Meanwhile, stir the garlic through the mayonnaise to make the aioli.
Allow the tortilla to cool a little before serving. Spread with the aioli and garnish with basil leaves.
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