Place the chicken thighs in the bottom of the slow cooker. Add the minced garlic, chicken broth, juice from one lemon, salt, and pepper. Lay two rosemary sprigs on top.
Cover and cook on low for 5 to 6 hours until the chicken is tender and reaches 165 degrees.
While the chicken cooks, preheat the oven to 425 degrees. In a bowl toss the carrots, parsnips, sweet potatoes, and onion with olive oil and the remaining salt and pepper.
Spread the vegetables on a baking sheet and tuck the remaining rosemary sprigs among them. Roast for 25 to 30 minutes, stirring once, until the edges turn golden.
Slice the second lemon into wedges. Serve the chicken with the roasted vegetables and lemon wedges on the side.