Remove the silver skin from the beef ribs and trim as needed. Coat the ribs with yellow mustard, then season generously on all sides with beef seasoning.
Preheat the smoker to 250°F and add hickory wood chunks.
Place the ribs on the smoker and cook for 2 hours. Spritz with apple cider vinegar, then continue spritzing every 45 minutes.
After about 4½ hours, or when the ribs have developed a dark bark and reach around 170°F internally, remove them from the smoker.
Place the ribs on butcher paper and add a few tablespoons of butter. Wrap tightly and return to the smoker.
Continue cooking for about 2 hours, or until the beef is probe tender.
Remove the wrapped ribs from the smoker and place them in a cooler to rest for 1–2 hours.
Roast the tomatillos, serrano pepper, onion, and garlic over high heat until softened and charred.
Let the roasted vegetables cool slightly, then add them to a blender with the cilantro, lime juice, and salt. Blend for 60–90 seconds.
Unwrap the rested beef ribs and shred the meat. Place the shredded beef in a bowl.
Heat a griddle or plancha to about 350°F. Warm each flour tortilla for 45–60 seconds per side.
Layer each tortilla with heated refried beans, white rice, shredded beef ribs, salsa verde, and Jack cheese.
Roll tightly into a burrito and place seam-side down on the griddle. Toast for 60–90 seconds, then flip and toast the other side.
Repeat with the remaining ingredients and serve warm.