Heat 2 Tbsp olive oil in a large skillet over medium heat. Add the chopped onion and the diced carrot (if using) and sauté, stirring occasionally, until the vegetables are softened, about 6 minutes.
Add the minced garlic, ground coriander, ground cumin, ground ginger, turmeric, ground cinnamon, and cayenne pepper (if using). Sauté, stirring constantly, about 30 seconds, until the spices are fragrant.
Stir in the 1/3 cup low-sodium chicken broth, the 1 (14.5 oz) can diced tomatoes, and the 1/3 cup diced dried apricots or whole raisins (if using). Season with salt and freshly ground black pepper to taste. Let the mixture come to a gentle simmer for 1–2 minutes.
Transfer the skillet mixture to the slow cooker. Add the diced chicken breasts (cut into 1 1/4-inch pieces) and the drained, rinsed chick peas. Gently toss to combine and evenly distribute the chicken and chick peas.
Cover the slow cooker and cook on low for 3 1/2 to 4 hours, until the chicken is cooked through and tender (internal temperature 165°F / 74°C if using a thermometer).
Stir in the 1 1/2 Tbsp fresh lemon juice, 1/4 cup chopped fresh cilantro, and the 1/4 cup chopped fresh parsley (if using). Taste and adjust salt and pepper if needed.
Serve the tagine warm (traditionally over rice or couscous) and garnish with extra cilantro if desired.