In a small bowl, stir together the smoked paprika, garlic powder, onion powder, kosher salt, black pepper, and dried thyme. This simple homemade rub is what gives the chicken its deep, savory flavor — no bottled seasoning mix needed.
Pat the chicken breasts dry with paper towels (dry surface = better seasoning adhesion). Rub the olive oil all over each breast, then coat generously on all sides with the spice rub, pressing it in so it sticks.
Scatter the quartered onion and minced garlic across the bottom of the slow cooker — they act as a natural rack and melt into the cooking juices. Arrange the seasoned chicken breasts in a single layer on top, then pour the chicken broth around (not over) the chicken so you don't wash off the rub.
Cover with the lid and cook on LOW for 3½–4 hours or HIGH for 2–2½ hours, until the chicken is cooked through (165°F / 74°C internal temperature) and shreds easily with a fork. Resist the urge to lift the lid — every peek lets out heat and adds 15–20 minutes to the cook time.
Transfer the chicken to a cutting board or large bowl (leaving the cooking liquid in the crock). Shred it with two forks, pulling along the grain into bite-sized pieces. Discard any onion pieces that are too soft to eat, or mash them into the liquid for extra flavor.
Return the shredded chicken to the slow cooker and toss it thoroughly with the cooking juices — this is the secret to juicy, flavorful shredded chicken instead of dry strands. Stir in the lemon juice if using, taste and adjust salt, sprinkle with fresh parsley, and serve.
