Step 1: Pat the chicken breasts dry with paper towels. If they are very thick, pound them to an even 3/4-inch thickness or cut them into 1-inch bite-sized pieces. Season generously with salt and black pepper on both sides.
Step 2: Heat the olive oil in a large skillet or pan over medium-high heat. Once shimmering, add the seasoned chicken to the hot pan. Cook for 4-6 minutes per side (if whole breasts) or until golden brown and cooked through, ensuring an internal temperature of 165°F (74°C). Remove the chicken from the skillet and set aside on a plate.
Step 3: Reduce the heat to medium. If there's a lot of oil left, drain some out, leaving about a tablespoon. Pour in the chicken broth, scraping up any browned bits from the bottom of the pan with a wooden spoon.
Step 4: Crumble in the entire block of Boursin Garlic & Fine Herbs cheese. Stir continuously until the Boursin is completely melted and the sauce is smooth and creamy.
Step 5: Stir in the heavy cream and cook for another 1-2 minutes, allowing the sauce to gently thicken. Taste the sauce and adjust seasonings as needed, adding more salt or pepper if desired.
Step 6: Return the cooked chicken to the skillet, spooning the creamy Boursin sauce over the top to coat. Garnish with fresh chopped parsley if desired. Serve immediately.