Peel potatoes and rinse under cold water. Keep submerged in a bowl of water until you're ready to proceed to prevent oxidation.
Shred potatoes on the large holes of a box grater. Put potatoes in a mesh strainer and risk off excess starch with cold water. Store submerged in water until you're ready to cook to keep them from turning gray.
Heat oil and butter in a 10- or 12-inch nonstick frying pan over medium heat until shimmering and butter has stopped foaming. Meanwhile...
Strain all water off the potatoes with the mesh strainer. Squeeze off as much water as you can. The drier they start out, the better they'll brown.
Sprinkle potatoes into the hot oil being careful not to splash yourself. I always squeeze excess water off the potatoes as I sprinkle to dry them a little bit more.
Season with a couple good pinches of salt and grinds of pepper. If you're adding the recommended spices, add them now, evenly over the top of the potatoes potatoes.
Cook without stirring or disturbing the potatoes for about 5 minutes. You can shake the pan somewhat during this time to make sure the browns aren't sticking. After the 5 minutes, use a spatula to lift up the potatoes slightly and check on their browning. If it's not yet to your liking, cook for a few minutes longer.
Decide whether you're going to try to flip them as a unit or break them up. Proceed accordingly.
Cook on the other side, or cook the mixed up potatoes until they are crisp to your liking, another 5 or 10 minutes total. Be careful, as they dry out in the hot pan, they'll start to brown faster and more aggressively. Turn your heat down a little if you need to prevent burning.
Serve immediately. Ketchup recommended.