In a large Dutch oven over medium, heat the oil until shimmering. Add the beef in an even layer and cook, stirring only once or twice, until well browned, 5 to 7 minutes. Add the garlic and ginger; cook, stirring, until fragrant and the aromatics begin to brown, about 1 minute. Add the tomatoes, 1 teaspoon salt and ½ teaspoon pepper. Cook, stirring, until the tomatoes have broken down, about 5 minutes.
Add 1½ quarts water and 1 tablespoon soy sauce. Bring to a boil over medium-high, scraping up any browned bits. Reduce to medium-low, partially cover and simmer, stirring occasionally, until the beef is tender, 12 to 15 minutes. In a small bowl, stir together the cornstarch and remaining 1 tablespoon soy sauce. While stirring the soup, gradually add the cornstarch mixture. Return to a simmer and cook, stirring, until thickened, about 1 minute.
A small stack at a time, add the wonton wrappers to the soup, separating the layers as you go. Once all the wrappers are added, cook, stirring, until the “noodles” are tender, about 2 minutes. Off heat, stir in the spinach, half the cilantro and the vinegar. Taste and season with salt and pepper. Serve sprinkled with the remaining cilantro and with additional soy sauce and vinegar on the side.
