Pat chicken breasts dry with paper towels and season generously with salt and black pepper on both sides. This creates a flavorful crust and prevents steam from making skin soggy—a CIA technique that elevates the final texture.
Heat olive oil in a large skillet over medium-high heat until shimmering but not smoking. Sear chicken for 3–4 minutes per side until golden brown, then transfer to your slow cooker (searing isn't absolutely necessary, but it adds incredible depth).
Add sliced onions and carrots to the slow cooker bottom, creating a vegetable bed for the chicken. This positioning allows vegetables to braise in chicken juices while supporting protein above liquid.
Combine chicken broth, white wine, minced garlic, thyme, rosemary, lemon juice, and Dijon mustard in a small bowl, whisking until mustard fully dissolves. Pour this mixture over chicken and vegetables, ensuring liquid reaches halfway up the chicken sides but doesn't completely submerge it.
Cover and cook on low for 6 hours, checking after 5.5 hours to ensure meat shreds easily with a fork. The beautiful slow cooker shredded chicken recipe reaches perfection when meat pulls apart without resistance and reaches an internal temperature of 165°F.
Remove chicken to a cutting board and shred with two forks, discarding any bones or cartilage. Strain cooking liquid, pressing vegetables gently to extract their essence, then return shredded chicken and strained liquid to the slow cooker.
Stir in fresh parsley just before serving to preserve its bright color and herbaceous aroma. Let the dish rest for 5 minutes, allowing flavors to settle and consolidate.