Pat the chicken dry on both sides with paper towels. Season with salt and pepper.
Melt the butter in a large dutch oven over medium-high heat. Add the chicken, skin-side down to the pan. Do it in batches so you don't overcrowd the pan. You want the skin to have a nice color to it. Brown the chicken for 5 minutes on one side, flip then cook for another 5 minutes. Remove the chicken to a large bowl and repeat until all chicken has cooked.
Once all the chicken has browned, lower the heat then add the olive oil and all the garlic and sauté the garlic for 5-10 minutes until golden. You'll want to constantly stir otherwise the garlic will burn.
Add the wine, turn up the heat, and using a wooden spoon, scrape the bottom of the pan to get up the browned bits. Return the chicken to the pot, with the liquid that has accumulated at the bottom of the bowl. Sprinkle the thyme over top, cover and simmer for 30 minutes.
After 30 minutes, remove the chicken and place on a plate.
In a small bowl, whisk together flour and 1/2 cup of the liquid from the pan. Pour back into the pan and whisk until the liquid thickens. Finally, whisk in the dark brown sugar and heavy cream. Turn off the heat. Season with additional salt and pepper, to taste.
Spoon sauce mixture and garlic over the plated chicken.
Serve hot with rice or vegetables.
Notes
*Highly suggest buying pre-peeled garlic to save you time!