Generously sprinkle the meat on all sides with salt and pepper. Lay the short ribs on the grill or large skillet on the stovetop and sear on all sides, until richly browned, 4 or 5 minutes. Remove to a baking sheet.
Heat canola oil in a large (7- to 8-quart) Dutch oven over medium heat. Add chiles and toast for 1 to 2 minutes, stirring constantly so chiles are fried well and change color.
Add onion and garlic and fry for 2 minutes, again stirring constantly.
Transfer fried ingredients to a food processor or blender and add red chile sauce. Puree until smooth with specks of chiles.
Return the sauce to the Dutch oven and add beer, broth, sauce, salt, and pepper. Place the short ribs and juices to the pan, nestling them into the liquid.
Set up grill for indirect grilling. Set the pot in the center of the grill and cook until the short ribs are fork-tender, 2 to 2 1/2 hours.
Carefully remove short ribs to a serving platter. Taste sauce and season with additional salt if necessary, and ladle it over ribs.