Sprinkle beef evenly with half the salt and pepper.
Heat the oil in a 5- to 6-quart Dutch oven over medium-high heat, add in the beef, and brown on all sides.
Remove the meat from the pan, add in the onion, jalapeno, and cumin; cook/stir until the onion and pepper are softened, about 3 minutes.
Return the meat to the pan and add the salsa and broth; bring to a boil, scraping up any browned bits stuck to the bottom of the pan.
Cover, reduce the heat to med-low, and simmer, stirring occasionally, until the meat falls apart, 2 1/2 to 3 hours.
Remove the meat from the pan and cover loosely with foil.
Taste the sauce for salt and pepper and add more if necessary.
Shred the beef, removing any fat, and serve with the sauce on the side.
**Do-ahead--at this point, you can combine the beef and sauce, cover, and refrigerate for up to 2 days; it actually tastes better when cooked in advance.
You can also freeze it in its sauce for up to 1 month.