Place the onion, carrots, and potatoes in the bottom of the slow cooker in a single-ish layer.

In a small bowl, combine the paprika, garlic powder, onion powder, dried rosemary, dried thyme, salt, and pepper.

Remove and discard any innards of the chicken. Place the chicken in a baking dish or sheet pan to make seasoning it easier and pat dry with paper towels. 

Loosen the skin around the breasts, you can use a long spoon or chopstick to help loosen the skin without ripping it. 

Rub the olive oil on the chicken. Rub the softened butter under the skin of the chicken breast. Then the spice rub over the chicken and under the skin on the breasts if possible.

Place the lemon pieces, garlic cloves, and fresh rosemary in the cavity of the chicken. 

Transfer the chicken on top of the vegetables in the slow cooker, breast side up. Cook on high for 4-5 hours or low for 7-8 hours. Use a meat thermometer to make sure the thickest part of the chicken thigh is at least 165F/75C to tell when the chicken is ready.

When done, place the chicken on a sheet pan under the oven broiler to crisp up the skin. Keep a close eye on it to ensure it does not burn. You can also add the vegetables to the sheet pan to broil as well.

Let the chicken rest for 5 to 10 minutes before carving. Serve the chicken with the vegetables and homemade gravy, if desired.

Strain the liquid left in the slow cooker through a fine-mesh strainer.

Heat a small saucepan over medium heat with 2 tablespoons of butter until melted. Whisk in 2 tablespoons of flour until smooth, around 30 seconds.

Slowly whisk in the strained liquid while whisking constantly. Cook while whisking until it has thickened to your liking, about 5 minutes. Season to taste with salt and pepper. Serve gravy with the chicken.