In a food processor, combine parsley and garlic. Pulse until chopped. Add softened butter and salt and pulse until well combined. Scrape out of food processor into a bowl.
Place chicken on a cutting board and pat dry. Remove giblets if necessary. Loosen skin by inserting fingers between the skin and meat, breaking any membranes connecting the skin to the meat.
Stuff garlic butter mixture evenly under skin. Working with 1-2 tablespoons at a time, stick a little mixture under the skin then spread out by pressing on top of the butter with your fingers under the skin or another hand on top of the skin. Repeat until all mixture is evenly used under skin over breast and legs.
Cut 1 head of garlic crosswise down the middle. Place one half of the garlic inside the chicken cavity.
Tie chicken legs together. Place a long piece of kitchen twine, about 3 feet long, on a surface. Place chicken in the center of the twine right at the top of the thigh. Take both pieces of twine in your hands and bring them down along the seam between the leg and breast. Loop twine inside the end of the leg and around, bringing both ends together and tying very tightly. See photos for examples.
Sprinkle chicken with a bit more salt.
Create a foil rack and place in the bottom of the slow cooker. Twist a long piece of foil into a "rope" then shape into a circle, or ball up 3-4 pieces of foil and place in a triangle or square shape in the bottom of the slow cooker. Place remaining half of garlic head in bottom of slow cooker.
Place chicken breast down on top of foil rack and cover.
Cook on low heat 4-5 hours or until internal temperature registers 160º F. See Note 2 for other cooking times.
Remove ceramic cooker from heating element. See Note 3 if your cooker does not come out. Carefully flip the chicken from breast down to breast up. Brush the 1 tablespoon oil all over chicken skin and preheat broiler. Place ceramic cooker in oven about 10" from heating element. Watching carefully, broil until skin is evenly browned, then remove from oven.
Remove chicken from cooker and place on a cutting board. Loosely tent with foil to rest. Replace cooker in slow cooker heating element and turn heat to high.
Make the gravy: Remove the garlic head. Sprinkle drippings with cassava flour and whisk well until smooth. Add in 1/2 cup stock and cook 10-15 minutes. If the mixture does not thicken to your liking, transfer to a saucepan and cook a couple minutes over medium heat, whisking constantly.
Carve chicken and serve with plenty of gravy.