Season chicken thighs with salt and pepper. Rub each piece generously with Dijon mustard and set aside.
In a Dutch oven or large deep skillet, heat 1 teaspoon olive oil over medium-high heat. Add diced bacon and cook until golden, about 5 minutes. Remove bacon and set aside. Drain excess fat, leaving about 2 tablespoons in the pan.
Add chicken thighs skin-side down and sear for 4–5 minutes per side until browned. Remove and set aside with the bacon.
Add remaining olive oil to the pan. Sauté shallots for 3 minutes, then add garlic and thyme and cook for another minute.
Pour in white wine to deglaze, scraping up the brown bits. Simmer until wine is reduced by half, about 3–4 minutes.
Stir in flour to thicken slightly, then pour in chicken broth. Bring to a boil.
Return chicken (skin-side up) and bacon to the pan along with juices. Reduce heat to medium-low, cover, and simmer for 15–20 minutes, until chicken reaches 165°F internally.
Uncover, stir in heavy cream and grainy mustard. Simmer uncovered on medium heat for 5–7 minutes, or until sauce thickens to your liking.
Stir in chopped parsley, adjust seasoning to taste, and garnish with thyme sprigs. Serve hot.