Pat dry the chicken thighs and place them in a bowl. Season generously with salt and ground black pepper. Add the Dijon mustard and rub well so that all the chicken pieces are thoroughly coated. Set aside for marinating while you prepare the rest of the ingredients.

Heat 1 teaspoon of extra-virgin olive oil in a large skillet or Dutch oven over medium-high heat. Add the diced bacon and cook until it turns golden brown, about 5 minutes. Use a slotted spoon to transfer the cooked bacon to a paper towel-lined plate, leaving about 2 tablespoons of bacon fat in the pan. Drain off any excess fat if necessary. Add the mustard-coated chicken thighs to the pan and brown them on all sides, about 4-5 minutes per side. Once browned, remove the chicken and reserve with the bacon.

Add the remaining olive oil to the same pan, then sauté the minced shallots over medium heat until softened, about 3 minutes. Stir in the minced garlic and fresh thyme leaves, cooking for another minute until fragrant. Pour in the dry white wine to deglaze the pan, scraping up all the browned bits from the bottom. Let it simmer and reduce until almost all the liquid has evaporated, about 3-4 minutes.

Sprinkle in the flour and stir well to combine with the aromatics. Pour in the chicken broth and bring the mixture to a boil. Once boiling, return the browned chicken thighs (skin side up), cooked bacon, and any accumulated juices to the skillet. Lower the heat to medium-low, cover, and let everything simmer until the chicken is cooked through, about 15-20 minutes. I like to use a meat thermometer to make sure the internal temperature of the chicken reaches at least 165ºF for optimal juiciness.

Uncover the pan and pour in the cold heavy cream and grainy mustard. Stir everything together and raise the heat to medium. Let the sauce boil until it thickens to your desired consistency. Taste and adjust with salt and pepper as needed. For a more intense flavor, I sometimes add a bit more grainy mustard at this stage.

Remove the skillet from the heat. Stir in the chopped parsley to add a burst of freshness. Serve the chicken and sauce garnished with fresh thyme sprigs for a bright, aromatic presentation.