Preheat the oven to 200°C/180°C fan.
Toss the sliced sweet potatoes with the oil and salt on a large baking tray, then spread them out into a single layer (you may need a second baking tray). Roast for 30–40 minutes, flipping them over halfway through, until starting to turn golden.
For the spiced mince, heat the oil in a large frying pan over a medium-low heat. Add the onion and cook for about five minutes until translucent. Add the mince, breaking it up with your spoon, and cook for a few minutes according to the packet instructions, or until the mince is no longer pink if using beef. Stir in the cumin, coriander, paprika, chilli powder and frozen (or fresh) sliced peppers. Stir until the peppers have defrosted and warmed through (about five minutes if using fresh, until softened). Tip into a bowl and set aside.
For the refried beans, return the same pan to the heat and add the drained beans along with 100 millilitres of the liquid reserved from the tin, the salt and cumin. Mash with a potato masher in the pan, loosening with more bean liquid as needed, to make a creamy, slightly chunky paste. Remove from the heat and set aside.
Mix together all of the salsa ingredients in a small bowl and set aside.
Once the potato nachos are roasted, top with spoonfuls of the refried beans, followed by a layer of the mince mixture and finally sprinkle over the grated cheese.
Return to the oven for 10–15 minutes until the cheese has melted and crisped up in places.
Remove from the oven, top with the salsa and some dollops of yoghurt, then serve.