Preheat the oven to 425 degrees. In a mixing bowl, toss the carrots, sweet potatoes, and red onion with 1 tablespoon olive oil, half the minced garlic, thyme, rosemary, salt, and pepper. Spread the vegetables on a baking sheet and roast for 30 to 35 minutes until the edges turn golden.
While the vegetables roast, season the chicken thighs with salt, pepper, lemon zest, and the remaining garlic. Place them in the slow cooker and pour the lemon juice and chicken broth over the top.
Cover and cook on low for 6 hours until the chicken reaches an internal temperature of 165 degrees and pulls away from the bone easily.
Remove the chicken from the slow cooker. Serve each thigh alongside a portion of the roasted root vegetables, spooning a little of the lemon garlic broth over the chicken.