Heat 2 teaspoons olive oil in a large nonstick skillet set over medium-high heat. Add the grated sweet potato and white sections of the green onions. Saute until the sweet potato is starting to soften, stirring constantly, about 3 minutes. Stir in the thyme, salt and pepper.
Add the remaining 2 teaspoons olive oil, then add the garlic, spinach and remaining green onions. Cook, stirring constantly, until the spinach is slightly wilted, about 1 minute.