Preheat your oven to 170–180°C.
Roast the peppers in a pan or under the grill. When their skin is completely blistered, put them into a bowl and cover with cling film. Leave to steam, then peel them and remove the seeds while still warm (do this over a bowl to keep all the cooking juices). Strain the juices through a sieve, pushing down on any skin, and reserve.
Season the aubergines with salt and leave in a colander for 10 minutes. Put the olive oil into a large pan on a medium heat. Fry the aubergines until coloured on both sides, then remove and season. Wipe down the pan, then pour in 1cm of olive oil and put the pan back on a medium heat. Add the potatoes and shallow-fry until light gold, soft around the edge but still a little raw in the middle. Season.
Grease a small tray or baking dish with olive oil. Put in all the potatoes in one layer, then add the aubergines, followed by the peppers, seasoning each layer. Cover with the tomato sauce, then roast in the oven for 10–12 minutes, until everything melds together and is cooked through. Season the lamb cutlets with salt and pepper. Put a pan on a medium heat. When hot, add the cutlets and fry until they get a nice golden brown crust then flip them over – 1-1½ minutes per side will give you a medium cutlet.
Drizzle the ajillo over the lamb cutlets to finish, and serve with the hot tumbet on the side.