In a slow cooker, place meat, salsa, onion and beef stock. Cook on high for 2-3 hours.
Remove meat from slow cooker, shred, and place back in the slow cooker for 30 minutes.
With a slotted spoon, remove meat and onions from the slow cooker and set aside.
In a large skillet over medium heat, melt butter. Place one tortilla in the bottom, then top with 1 cup cheese and 1/3 of the meat mixture and place a second tortilla on top. Cook until cheese starts to melt and the tortilla starts to brown (about 3-4 minutes), and then flip the quesadilla and brown the other side (about 3-4 minutes).
Repeat two more times.
Cut into triangles and serve warm with chipotle aioli.
Notes
We sprinkled ours with cotija cheese, just like the restaurant, but it would be good with Parmesan or mozzarella on top, too.
How to turn this into a freezer meal:Add short ribs, salsa, and onion to a gallon-sized freezer bag. Squeeze out as much air as possible and seal bag closed. Place freezer bag into freezer and it will last 60-90 days. When ready to use, spray inside of slow cooker with non-stick cooking spray. Dump ingredients from bag into slow cooker and add 2 cups of beef stock in with the frozen food. Place the lid on top. Cover and cook on LOW heat for 6-8 hours (or HIGH heat for 3-4 hours). Follow the rest of the instructions as written.