Place Hatch chiles directly on the grates of a gas stove. Cook over medium heat, flipping with tongs occasionally, until blackened and charred, about 5 minutes. Place in a sealed plastic bag and allow to cool, 7 to 8 minutes.

Peel off charred skins, remove seeds, and cut 1/2 of the chiles into 1-inch squares. Set aside. Place remaining chiles in a food processor and process until finely chopped. Add processed chiles to chopped chiles. Set aside.

Combine pork cubes, water, and salt in a Dutch oven. Cover and cook over medium heat for 20 minutes, stirring every 5 minutes. Uncover, raise heat to medium-high, and cook, stirring constantly until the water evaporates and the pork browns in its rendered fat, 15 to 20 minutes. Remove pork and set aside.

Heat oil in the Dutch oven. Add onion; cook and stir until soft and translucent, 5 to 7 minutes. Add garlic and cumin and cook until fragrant, about 1 minute. Stir in flour and cook for 1 to 2 minutes. Add chiles, pork, chicken broth, canned tomatoes, salt, and pepper. Bring to a boil. Reduce heat to low, cover, and simmer, stirring occasionally, until pork cubes are fork-tender, about 1 1/2 hours.