Preheat oven to 375°F °F (190°C). Sprinkle chicken skin all over with salt and pepper. Melt butter in a Dutch oven over medium heat. Place the chicken breast-side down until the skin is golden, about 5 minutes. Flip and sear the other side until browned, another 5 minutes. Remove chicken to a plate.
Add onions and garlic cloves to the pan, cooking and stirring until they soften and begin to take a little color. Make sure you scrape the browned bits off the bottom of the pan. Add 1 tablespoon of water if the bottom starts to burn.
Add sweet potatoes and stir until covered with butter and chicken drippings. Cover and cook for 5 minutes, stirring occasionally to keep the onions from burning,
Flatten out the sweet potatoes to an even layer and lay the chicken on top, skin-side up. Make sure to spread the chicken as flat as you can so as much skin is facing up as possible, which allows for more crisping.
In a bowl, combine mustard, balsamic vinegar, brown sugar, thyme, and salt. Stir well. Spoon over every exposed surface of chicken.
Place chicken in the oven and roast until its internal temperature reaches 160°F (71°C), which should take about 40 to 50 minutes. Make sure to test the thickest part of the breast and thigh to make sure they are both cooked through. If the breasts are done first, carve them off and return the rest of the pot to the oven until the thighs have reached 160°F (71°C).
Remove chicken from oven and allow to rest for 10 minutes before serving. The internal temperature will increase a few degrees as it rests, taking it to about 165°F (74°C) before it cools.