1. Add chopped potatoes and sweet potatoes to a pot with enough water to cover them. Bring to a boil, then take off the heat and drain. Set aside.
2. If you've cooked bacon (like we often do on Sundays), discard all but about 1 tablespoon of the fat, and add 2 tablespoons of olive oil (if you don't eat bacon or don't want to use bacon fat, use 1 tablespoon butter plus 2 tablespoons olive oil, or use all olive oil). Heat whichever type of fat(s) you want to use over medium-high heat, and add the chopped onion and garlic. Cook, stirring frequently, until very soft and fragrant, about five minutes.
3. Add the potatoes, and cook for another 8-10 minutes. Alternate stirring the contents of the pan around so nothing burns (well to be honest, we like it when the onions burn a bit), and pressing everything down with a spatula so the potatoes get somewhat brown.
4. A liberal sprinkling of coarse sea salt and several grinds of the pepper mill finishes these potatoes off nicely; serve with eggs and optional bacon, doused with a little hot sauce, if you like.