Put the minced beef, onion and garlic in a medium non-stick saucepan and cook over a high heat for five minutes, stirring with two wooden spoons to break up any clumps of meat. Stir in the cumin, coriander and chilli and cook for two minutes more, stirring constantly. Add the tomato purée, sugar and beef stock and bring to a simmer. Cover the pan and leave to simmer gently over a low heat for 30 minutes. Remove the lid and stir the chilli mixture occasionally.
While the beef is cooking, prepare the tortilla bowls. Preheat the oven to 180C/350F/Gas 4. Take a sheet of foil about 1 metre/40in long and scrunch it up into a ball about 10cm/4in in diameter. Place it in the centre of a large baking sheet.
Take a tortilla and brush the centre on one side with a little of the oil – this will help prevent it sticking to the foil. Drape the tortilla over the ball of foil, oil-side down, pinching and loosely pleating it to create a bowl shape. Bake for five minutes until the bowl shape is set and the tortilla is lightly crisped.
Take the tortilla out of the oven and carefully remove it from the foil – it should be just cool enough to handle. Place the tortilla on an upturned tumbler and press to create a flat base on which to turn the tortilla once cold. The tortilla should still be warm enough to mould to the shape of the glass. Leave to cool while you make the next bowl in the same way. Put each upturned tortilla on a plate as soon as it is ready.
Remove the lid from the pan of beef and turn the heat up high. Cook for a further 4–5 minutes, stirring constantly, until most of the liquid has evaporated and the beef is looking fairly dry. Take the pan off the heat.
Toss the lettuce with the tomatoes, cucumber, spring onions and lime juice. Divide the salad between the tortilla bowls and season with black pepper, then top with the hot mince. Coarsely grate some cheddar over each serving and add some crème fraîche and salsa. Tuck in while the beef is warm.