Place the chicken thighs in a large bowl. Season them generously with salt and freshly ground black pepper. Add the Dijon mustard and use your hands to rub it all over the chicken, ensuring each piece is thoroughly coated. Set the chicken aside to marinate while you move on to the next steps.

Heat 1 teaspoon of extra-virgin olive oil in a large skillet, braiser, or Dutch oven over medium-high heat. Add the diced bacon and cook until golden brown, about 5 minutes. Remove the bacon with a slotted spoon and transfer to a paper towel-lined plate to drain. If there's excess fat in the pan, drain most of it, leaving about 2 tablespoons. Add the marinated chicken from Step 1 to the pan and brown on all sides, about 4–5 minutes per side. Once browned, remove the chicken and reserve with the bacon.

Add 1 tablespoon of extra-virgin olive oil to the pan if needed. Add the minced shallots and sauté over medium heat until softened, about 3 minutes. Stir in the minced garlic and cook for another minute until fragrant. Add the fresh thyme leaves, stirring to combine. Pour in the dry white wine, scraping the browned bits off the bottom of the pan to deglaze and infuse the sauce with flavor. Cook until the wine is almost evaporated, about 3–4 minutes. I always take my time with this step—scraping up those browned bits gives the sauce amazing depth.

Sprinkle the flour over the aromatics and mix well. Gradually pour in the chicken broth, stirring constantly to avoid lumps. Bring the mixture to a boil. Once boiling, return the browned chicken (skin side up), cooked bacon, and any accumulated juices to the pan. Lower the heat to medium-low, cover, and simmer until the chicken is fully cooked and tender (internal temperature at least 165ºF), about 15–20 minutes.

Uncover the pan and stir in the heavy cream and grainy mustard. Increase the heat to medium and let the sauce boil gently until it thickens to your desired consistency. Taste the sauce and adjust the seasoning with extra salt and freshly ground pepper if needed. For a more luxurious flavor, I sometimes add a little extra cream at this stage.

Turn off the heat and stir in the chopped fresh parsley for brightness. Serve the chicken hot, garnished with thyme sprigs on top for an aromatic finish.