Preheat a skillet over medium heat and add the olive oil.
Add the tomatillos, quartered onion, garlic cloves, and jalapeño peppers to the skillet. Cook for 5-7 minutes, turning occasionally, until the tomatillos and vegetables are softened and slightly charred.
Transfer the cooked tomatillos, onion, garlic, and jalapeños to a blender.
Add the cilantro leaves, ground cumin, dried oregano, salt, black pepper, chicken broth, and lime juice to the blender.
Blend until the mixture is smooth and well combined, forming the verde sauce.
Place the chicken breasts in the bottom of the slow cooker.
Pour the verde sauce evenly over the chicken breasts.
Cover and cook on low for 4 to 4.5 hours, or until the chicken is cooked through and tender.
Once cooked, shred the chicken directly in the slow cooker using two forks and stir to coat the shredded chicken with the verde sauce.
Serve the slow cooker chicken verde warm with your choice of rice, tortillas, or toppings.