Layer the base: In a slow cooker or oven-safe dish, scatter the sliced onion. Place the chicken on top.
Mix the flavor: In a bowl, stir together salsa verde, garlic, cumin, salt, pepper, and lime juice.
If using green chiles or broth, add them now.
Dump and go: Pour the salsa mixture over the chicken, coating it evenly.
Cook it low and slow (slow cooker): Cover and cook on Low for 4–5 hours or on High for 2–3 hours, until the chicken is fork-tender and reaches 165°F.
Or bake it (oven): Cover tightly with foil and bake at 375°F for 30–35 minutes (breasts) or 35–45 minutes (thighs), until cooked through.
Instant Pot option: Add everything to the pot with 1/4 cup water. Cook on Manual High for 10 minutes (breasts) or 12 minutes (thighs). Natural release for 5 minutes, then quick release.
Shred: Transfer the chicken to a board and shred with two forks.
Return it to the sauce and toss to coat. Taste and adjust seasoning with more salt or lime.
Serve: Spoon into tortillas, over rice, or onto salads. Top with cilantro, avocado, and any extras you love.