Place potatoes, carrots, and onion in the slow cooker and sprinkle with half the salt, pepper, and half the herbs.
Pat chicken dry, season with remaining salt, pepper, paprika, and herbs, then place on top of vegetables.
Pour garlic, olive oil, and chicken broth over everything.
Cover and cook on low for 6–7 hours or high for 3–4 hours, until chicken reaches 165°F and vegetables are tender.
If you want a thicker sauce, whisk cornstarch with water, stir into the cooker, and cook on high 10–15 minutes.
Serve pieces of chicken with potatoes and carrots, spooning the pan juices over each plate.