Cut potatoes into 1/2-inch pieces. Core and chop tomatoes. In a 5- to 6-quart pan, combine potatoes, tomatoes, broth, chilies, and garlic. Bring to a boil over high heat; cover, reduce heat, and simmer until potatoes are tender when pierced, 12 to 15 minutes.
While potatoes simmer, trim off and discard excess fat from pork. Cut pork crosswise into 1/4-inch-wide strips, then cut strips in half. To a 10- to 12-inch nonstick frying pan, add oil and pork; cook over medium-high heat, stirring often, until pork is lightly browned, about 7 minutes. Remove from heat; set aside.
When potatoes are tender, stir in pork; simmer just long enough to warm meat through, about 2 minutes. Add 1 or 2 drops of hot sauce, if desired.
This stew from Stella Perea of Corrales, New Mexico, is typical of native New Mexican dishes. Perea, who grew up in New Mexico, owns Perea's restaurant, where she serves items such as blue-corn enchiladas and vegetarian tamales. This recipe was handed down from her grandmother. Perea uses lean pork or round steak--we substituted smoked pork because we like its flavor and, since it's cooked, it saves time. She serves the quick chili stew as a meal on its own with her homemade tortillas or adds pinto beans and Spanish rice as accompaniments.