Prep the vegetables: Halve the potatoes, chop the carrots, and slice the onion. Keep pieces roughly the same size so they cook evenly.
Season the chicken: Pat the chicken dry.
Season both sides with salt, pepper, paprika, thyme, rosemary, and garlic powder if using.
Build the base: Add the potatoes, carrots, and onion to the bottom of the slow cooker. Sprinkle with a pinch of salt and pepper. Add the bay leaf.
Layer the chicken: Place the seasoned chicken on top of the vegetables.
Scatter the minced garlic over the chicken.
Add liquids: Pour in the chicken broth. Drizzle with olive oil or dot with butter. Add lemon zest and 1 tablespoon lemon juice.
Cook low and slow: Cover and cook on Low for 6–7 hours or on High for 3–4 hours, until the chicken is tender and the potatoes are soft when pierced.
Add green beans: In the last 30–45 minutes of cooking, stir in the green beans so they become tender-crisp without overcooking.
Adjust seasoning: Taste the broth and add more salt, pepper, or lemon juice as needed to brighten the flavors.
Optional thickening: If you want a slightly thicker sauce, remove 2 tablespoons of cooking liquid, whisk in 1–2 teaspoons cornstarch, then stir back into the slow cooker for 10–15 minutes on High.
Serve: Spoon the chicken and veggies into bowls, drizzle with the cooking juices, and finish with chopped parsley.