Pat the chicken breasts dry and season both sides with salt and pepper.
Heat the olive oil and butter in a large skillet over medium-high heat until the butter is melted and the pan is hot.
Add the chicken to the skillet and sear 5 minutes per side, until golden brown.
Pour 1/2 cup of the chicken broth into the skillet, cover, and cook 5 to 6 minutes more, until the chicken is cooked through; then remove the chicken to a plate.
Add the diced onion to the skillet and cook 3 to 4 minutes, stirring, until softened.
Add the remaining chicken broth and simmer for 2 minutes to deglaze and concentrate the flavors.
Stir in the creole mustard, honey, heavy cream, and cayenne and simmer 3 to 4 minutes, stirring, until the sauce thickens slightly.
Return the chicken to the skillet and cook 1 to 2 minutes to warm through and coat with sauce.
Sprinkle the chopped thyme over the chicken, taste the sauce, and adjust seasoning with salt and pepper if needed; serve.