Season the chicken breasts on both sides with salt and pepper.
Heat the olive oil and butter in a large skillet over medium-high heat until butter is melted and hot.
Add the chicken to the skillet and cook about 5 minutes per side until golden brown.
Add 1/2 cup of the chicken broth to the skillet, cover, and cook 5 to 6 minutes more until the chicken is cooked through; remove the chicken to a plate and keep warm.
Add the diced sweet onion to the skillet and cook 3 to 4 minutes, stirring, until softened.
Add the remaining chicken broth to the skillet and simmer about 2 minutes to deglaze and reduce slightly.
Stir in the Creole mustard, honey, heavy cream, and cayenne; simmer 3 to 4 minutes 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.