Place the sliced onion in a 6-quart slow cooker and set the beef on top.
Pour the salsa verde over the beef and turn the roast once to coat it.
Cover and cook on low until the beef shreds easily, 7 1/2 to 8 hours.
Transfer the beef to a board, discard large fat pockets and shred it with two forks.
Skim the sauce, return the beef to the cooker and toss it through the onion and salsa for 10 minutes.
Warm the tortillas in a dry skillet until flexible and lightly spotted, about 20 seconds per side.
Fill each tortilla with drained salsa verde beef and serve two per person.