Prepare the chicken: Season the chicken breasts generously with salt and pepper. Pat them dry with paper towels for even browning.
Sear the chicken: Heat the olive oil in a large skillet over medium-high heat. Sear the chicken breasts for about 3-4 minutes per side, until nicely browned. Tip: Don't overcrowd the pan. Work in batches if necessary for even searing.
Sauté the garlic: Add the butter to the skillet and melt it. Add the minced garlic and sauté for about 30 seconds, until fragrant. Tip: Don't burn the garlic; it will become bitter.
Deglaze the pan: Pour in the white wine, scraping up any browned bits from the bottom of the pan. Let it simmer for a minute or two, allowing the alcohol to cook off.
Add the broth and Boursin: Stir in the chicken broth. Bring to a gentle simmer. Reduce heat to low, add the Boursin cheese, and stir until it's completely melted and incorporated into the sauce.
Simmer the chicken: Return the seared chicken breasts to the skillet. Reduce the heat to low, cover, and simmer for about 10-15 minutes, or until the chicken is cooked through and the juices run clear. Tip: Use a meat thermometer to ensure the chicken reaches an internal temperature of 165°F (74°C).
Stir in the herbs: Stir in the fresh basil and thyme. Season with additional salt and pepper to taste. If you prefer a thicker sauce, whisk in a tablespoon of all-purpose flour at this stage.
Serve: Serve the chicken immediately over your favorite pasta, rice, or mashed potatoes. Garnish with extra fresh herbs if desired.