Step 1: Season and Sear the Chicken
Pat the chicken completely dry with paper towels. This is crucial for crispy skin. Season both sides generously with salt and pepper. Heat the olive oil in a large, heavy-bottomed skillet (cast iron or stainless steel) over medium-high heat. Once hot, add the chicken thighs skin-side down (or breasts smooth-side down). Sear without moving for 6-8 minutes, until the skin is deeply golden brown and crisp. Flip and sear for 2-3 minutes on the other side. Transfer the chicken to a plate. It will not be fully cooked.

Step 2: Build the Aromatic Base
Reduce the heat to medium. Add 1 tablespoon of the butter to the skillet. Once melted, add the minced garlic and thyme. Cook for 1 minute until fragrant, being careful not to burn the garlic.

Step 3: Create the Sauce Base
Pour in the chicken broth to deglaze the pan, scraping up all the flavorful browned bits (fond) from the bottom. Let it simmer for 1-2 minutes. Reduce heat to medium-low. Whisk in the heavy cream, Dijon mustard, honey, whole-grain mustard (if using), and Worcestershire sauce until smooth.

Step 4: Simmer and Combine
Bring the sauce to a gentle simmer. Nestle the seared chicken back into the skillet, skin-side up, along with any accumulated juices. Spoon some of the sauce over the top of the chicken.

Step 5: Cook Through
Cover the skillet and let it simmer gently for 12-15 minutes (for thighs) or 8-10 minutes (for breasts), until the chicken is cooked through (internal temperature of 165°F / 74°C for breasts, 175°F / 80°C for thighs).

Step 6: Thicken the Sauce (Optional)
If you prefer a thicker sauce, remove the cooked chicken to a clean plate. Increase heat to medium and let the sauce simmer uncovered for 2-3 minutes to reduce. For a quicker thicken, whisk in the cornstarch slurry and simmer for 1 minute until glossy and thickened.

Step 7: Finish the Sauce
Remove the skillet from heat. Stir in the remaining 2 tablespoons of cold butter, one piece at a time, swirling the pan until each is fully melted and incorporated. This (monter au beurre) gives the sauce a luxurious, restaurant-quality silky finish and shine.

Step 8: Garnish and Serve
Return the chicken to the skillet to coat in the finished sauce. Garnish with fresh thyme or parsley and a pinch of flaky sea salt. Serve immediately, spooning extra sauce over each piece.