In a 6-quart slow cooker, arrange potatoes, celery, carrots, onion, 3 garlic cloves, 3 rosemary sprigs, and 4 thyme sprigs. Place most of the vegetables towards the edges so that the chicken can be placed in the center.
Remove the giblets and neck from the chicken. Dry the outside and inside surfaces with paper towels. Massage the cavity with ½ teaspoon salt and ¼ teaspoon pepper. Add 1 sprig of rosemary, 2 sprigs of thyme, 1 garlic clove, and lemon wedges to the chicken's cavity.
Tuck the wings back and tie the legs together with butcher's twine.
In a small bowl, combine 2 tablespoons melted butter, 2 teaspoons salt, paprika, and ¼ teaspoon black pepper. Set the paste aside. If the butter hardens, microwave it in 5-seconds intervals to melt.
Place the chicken on a sheet pan breast-side down. Brush the seasoning paste over the bottom. Flip over and brush the top of the breast, wings, and thighs. Place the chicken breast-side up on the bed of vegetables.
Add ½ cup chicken stock to the pot. Cover and cook on the “High” setting for about 4 to 5 hours, or “Low” setting for about 7 to 8 hours, or until the breasts reach an internal temperature of 160 to 165ºF (71 to 74ºC), and thighs reach about 170ºF (77ºC). The potatoes should be fork-tender.
Place a large spoon in the chicken's cavity, use it to tilt, and drain the juices into the pot. Transfer the chicken to a cutting board and rest for 15 minutes before carving. See notes for how to make a crispier skin (optional).
Use a large spoon to scoop the vegetables into a platter or bowl, cover with foil to keep warm.
Gravy
Transfer chicken drippings to a measuring cup. Add additional chicken stock until the volume reaches 2 cups.
Heat a medium-sized pan over medium heat. Melt the butter and then whisk in flour. Whisk and cook until a pale yellow roux forms, about 1 to 2 minutes.
Gradually whisk in 2 cups of chicken drippings. Turn the heat up to medium-high, continuously stir until thickened, about 1 to 2 minutes. Add more chicken stock if desired to thin the sauce, it will thicken more as it cools. Season gravy with salt and pepper.
To Serve
Once the chicken has rested, carve it into smaller pieces and slice the breast. Serve with vegetables, lemon slices, and gravy on the side.
For Crispy Skin: Carefully transfer the chicken to a foil-lined baking tray with a wire rack on top. It helps to place a large spoon inside the cavity to lift it out of the pot. Brush the surface with olive oil and broil 10-inches away from the top of the oven until the skin browns, about 5 to 10 minutes.
To Brown the Vegetables: Place the vegetables on a foil-lined sheet tray. Broil 10-inches away from the top of the oven until lightly browned, about 8 to 10 minutes.
Make it Gluten-Free: For the gravy, substitute all-purpose flour with gluten-free flour or cassava flour. The liquid for the gravy can also be thickened with a cornstarch slurry. Combine 2 tablespoons of cornstarch with ¼ cup of cold water. Bring the 2 cups of chicken liquid/stock to a boil over medium-high heat, then slowly whisk in the slurry until thickened, about 1 minute.