Pat the chicken breasts dry and season both sides with salt, pepper, half the minced garlic, rosemary, and thyme.
Place the chicken in the slow cooker and pour the chicken broth over the top. Squeeze the juice from one lemon over the chicken and add the remaining lemon sliced into rounds on top.
Cover and cook on low for 4 to 5 hours until the chicken reaches an internal temperature of 165°F.
While the chicken cooks, preheat the oven to 425°F. Toss the potato pieces with the remaining 2 tablespoons olive oil, the rest of the minced garlic, rosemary, thyme, salt, and pepper.
Spread the potatoes in a single layer on a baking sheet. Roast for 30 to 35 minutes, stirring once, until golden and crisp on the edges.
Remove the chicken from the slow cooker and let it rest for 5 minutes. Slice or serve whole alongside the roasted potatoes. Sprinkle everything with fresh parsley before serving.