Heat oil in a large Dutch oven or large pot over medium heat.
Spread flour into a wide, shallow dish; add pork and turn to coat, shaking off excess.
Cook coated pork in hot oil until completely browned, 5 to 7 minutes. Stir onion and garlic in with the pork; continue cooking and stirring until the onion softens, about 5 minutes. Pour diced tomatoes, green chilies, and 2 tablespoons cilantro over the pork mixture; stir. Place a cover on the Dutch oven and simmer the mixture until pork is tender and no longer pink in the center, about 40 minutes.
Whisk cold water and cornstarch together in a small bowl; stir into the liquid in the Dutch oven and continue cooking until the sauce thickens, 5 to 10 minutes.
Remove Dutch oven from heat; let dish rest 10 to 15 minutes. Ladle into bowls and top with cheese and desired amount of cilantro to serve.