Beef Cheeks for Barbacoa and More
When I was a little boy in South Texas, barbacoa was one of the Mexican dishes that was a special tradition. My earliest recollection of barbacoa de cabeza, or beef-head barbacoa, was prepared at a neighboring ranch. They had a permanent earth oven, basically a hole in the ground on one end of a concrete patio. The seasoned heads were covered in wet corn husks then placed in burlap bags, and buried with layers of coals and dirt and cooked for 20+ hours. It's super tender and flavorful, but I like a smokey flavor, and I'm not digging a hole in the backyard. That said, you can use this basic technique and do all your cooking in an oven, (or a Dutch oven) and the results will still be amazing.
I use beef cheeks for barbacoa and for shredded beef in several recipes. It's a lot of work trimming them because they have a lot of fat, sinew, and sliver skin. I do inject them for more flavor, but injecting is not mandatory. My seasonings are salt and pepper as a minimum, but I generally go a little farther. Follow along for a recent cook, and I'll throw in some options you might want to explore.
For this barbacoa, I'll be using a jazzy beef broth for injecting, seasoning with cracked pepper, and Goldee's Brisket Rub. An alternate seasoning would be Kosher salt, or seasoned salt, cracked pepper, and granulated garlic. If you want a sweet profile, any rub you like on a pork butt or pork ribs will work just fine.
I used an indirect set up on my kettle grill, and prefer lump charcoal over briquettes. Whatever kind of grill or smoker you have will work just fine. The pit temp was 250° and never got above 275°. Because you are rendering fat, I would not go above 300°. There were a couple of smaller pieces that I held back, and put on after 90 minutes so they would not overcook.
Here are all the pieces ready for the pressure cooker, but you could wrap them in foil with a couple ounces of liquid, or put them into a covered foil pan with liquid and braise them in the oven until very tender. Either braising option will take 2 or 3 hours. On the other hand, when using my 'traditional' pressure cooker only takes 45 total minutes (see the pressure times below)