Step 1: Pat chicken breasts dry with paper towels and season generously with salt and pepper on both sides. If desired, pound them to an even 1/2-inch thickness.
Step 2: In a large skillet or pan over medium-high heat, cook the bacon until crispy. Remove bacon from the pan, set aside on a paper towel-lined plate, and chop into pieces once cool. Reserve about 1 tablespoon of bacon fat in the skillet, draining any excess.
Step 3: Add olive oil to the same skillet with the reserved bacon fat over medium-high heat. Sear the chicken breasts for 3-5 minutes per side, or until golden brown and cooked through (internal temperature 165°F/74°C). Remove chicken from the skillet and set aside on a plate, tented with foil.
Step 4: Reduce heat to medium. Add the chopped onion to the skillet and sauté for 3-4 minutes until softened and translucent. Add the minced garlic and fresh thyme, cooking for another minute until fragrant.
Step 5: Pour in the chicken broth, scraping up any browned bits from the bottom of the pan. Bring to a simmer and let it reduce slightly, about 2-3 minutes.
Step 6: Whisk in the heavy cream and Dijon mustard. Continue to simmer gently for 2-3 minutes, stirring occasionally, until the sauce thickens slightly.
Step 7: Return the cooked chicken breasts to the skillet, spooning the sauce over them. Stir in the chopped crispy bacon. Cook for another minute to heat through.
Step 8: Garnish with fresh chopped parsley, if using, and serve immediately.