Warm the olive oil in a large skillet over medium-high heat until it glistens.
Season the chicken breasts on both sides well with salt and pepper.
Place the chicken in the skillet and cook each side for about 6 to 7 minutes until nicely browned and fully cooked (internal temperature should reach 165°F). Remove the chicken and set aside.
In the same pan, toss in the sliced onions and sauté for 3 to 4 minutes, stirring now and then until they soften.
Add the minced garlic next and cook for another 1 to 2 minutes until aromatic.
Pour in the chicken broth, scraping the skillet’s bottom to lift any flavorful bits stuck.
Mix in the heavy cream, Dijon mustard, and dried thyme until the sauce is uniform.
Return the chicken breasts back to the skillet and ladle the sauce over them.
Turn the heat down to low, cover the skillet, and let it simmer for 5 to 10 minutes until the sauce thickens slightly.
Sprinkle freshly chopped parsley on top before serving immediately.