Cook the sweet potato noodles in a large pot of boiling water for 4 to 5 minutes. Immediately drain and rinse thoroughly under cold water. Be sure not to overcook the noodles, or they will lose their chewy texture.
Blanch the spinach in boiling water. Rinse immediately under cold water, squeeze the water from the leaves and form into a ball, and then cut the ball in half. Combine the spinach, half the garlic, ½ teaspoon of the sesame oil, and ¼ teaspoon salt in a small bowl. Set aside to marinate.
Heat the vegetable oil in a large skillet over medium-high heat. Add the pork or beef, the remaining garlic, 1 teaspoon of the soy sauce, and 1 teaspoon of the sesame oil. Stir-fry until the beef is cooked, 3 to 4 minutes. Add the onion, mushrooms, and carrot and cook until the onion is translucent, about 3 minutes. Add the green onions and stir-fry for another minute. Remove from the heat.
In a large bowl, thoroughly combine the noodles, beef mixture, spinach, remaining ¼ cup soy sauce, 1 tablespoon sesame oil, and the sugar. Serve warm, sprinkled with sesame seeds.