Heat a large saute pan over medium-high heat. Add the bacon pieces and cook until crispy, about 5 minutes. Remove the bacon from heat and drain all but 1 tablespoon of the fat. Reserve the remaining bacon drippings.

Add the chopped onion and season with ½ teaspoon salt. Reduce heat to medium and cook until caramelized, about 20 minutes. If the pan becomes too dry, add a little bit of water.

Add 1 cup chicken broth and 1 teaspoon fresh thyme to the caramelized onions. Bring to a boil, reduce heat to medium-low and simmer for 5 minutes.

Meanwhile, make the chicken. Coat the chicken in flour, shaking off the excess. Season both sides with salt and pepper. Heat 1 tablespoon of the reserved bacon drippings in a saute pan over medium heat. Add the chicken and cook until golden brown on both sides. Remove the chicken from the pan and put in the pan with the sauce. Cover the pot and continue to simmer until the chicken is fully cooked. Remove the chicken and keep warm.

Add the heavy cream and stone mustard and stir to combine. Season the sauce with salt and pepper and pour over the chicken. Sprinkle the cooked bacon on top and serve immediately.