Peel the sweet potatoes and grate them by hand or with the grating disk of a food processor; you should have about 5 packed cups; save any extra for another use.
Put 2 tablespoons of the oil in a large skillet over medium-high heat. When it’s hot, add half the sweet potatoes, spread them out in an even layer, and sprinkle with half of the garlic and some salt and pepper. Cook, without stirring, until the potatoes begin to brown on the bottom and release easily from the skillet, 3 to 5 minutes.
Continue cooking, stirring every 2 to 3 minutes, until the potatoes are mostly golden brown and tender but not mushy; begin checking after about 5 minutes. When they’re ready, transfer them to a serving plate.
Repeat with the remaining ingredients. Add the second batch of sweet potatoes to the first and toss to combine. Taste, adjust the seasoning, toss again, and serve.