Add the quartered onion to the pot and cook for 3 minutes until slightly softened. Add minced garlic and cook for 1 minute more until fragrant.
Deglaze the pot by pouring in the beef broth, scraping up any browned bits from the bottom.
Return the beef to the pot. Add the apple cider vinegar, lime juice, chili powder, cumin, oregano, salt, pepper, minced chipotle peppers, adobo sauce, and bay leaves. Stir gently to combine.
Secure the lid and set the vent to Sealing. Select Manual/Pressure Cook (High Pressure) for 60 minutes.
When the cooking cycle finishes, allow a Natural Pressure Release (NPR) for 15 minutes, then carefully quick release any remaining pressure.
Remove the beef chunks and place them in a large bowl. Discard the bay leaves.
Shred the beef using two forks. Pour about 1/2 cup of the reduced cooking liquid over the shredded beef and toss to coat. Add more liquid if needed for moisture.
Serve immediately in warm tortillas for tacos.
Notes
For deeper flavor, you can marinate the beef chunks in the spices and vinegar mixture for 2 hours before cooking.
If you prefer a thicker sauce, mix 1 teaspoon of cornstarch with 1 tablespoon of cold water and stir this slurry into the boiling liquid during the reduction step.
This barbacoa freezes well. Cool completely before storing in an airtight container for up to 3 months.