1. Peel and chop onion. Peel and chop carrots and potatoes into large chunks. Slice lemon. Crush rosemary.
2. Heat 1/2 of the olive oil in a large skillet over medium heat. Season chicken thighs with salt and black pepper and transfer 1/2 of them to the skillet.
3. Brown chicken, approximately 3 minutes per side, and transfer to a platter.
4. Repeat process with remaining olive oil and chicken thighs. Once browned, transfer remaining chicken thighs to the platter with the first batch.
5. Deglaze skillet by adding the chicken broth and gently scraping the bottom with a spatula to incorporate the flavorful brown bits into the liquid.
6. Remove from heat and reserve the deglazing liquid. Set aside.
7. Add garlic, onion, carrots, and potatoes to a slow cooker crock and arrange the browned chicken thighs on top.
8. Spread 2/3 of the lemon slices over the chicken and pour the chicken broth from the skillet on top.
9. Sprinkle with the crushed rosemary leaves and season with additional salt and black pepper, if desired.
10. Cover and cook on high for 3 hours or low for 6 hours. The chicken is cooked through when a meat thermometer inserted (avoiding the bone) reads 165F.
11. While the chicken cooks, chop the parsley.
12. When cook time is complete, discard lemon slices and serve immediately with chopped fresh parsley and the remaining lemon slices cut into small wedges for garnish.