Season both sides of chicken liberally with salt and pepper.

Over medium-high heat, melt the butter and extra-virgin olive oil until shimmering. Brown both sides of the chicken (about 4 minutes per side). Remove chicken to a plate.

In the same pan, sauté the garlic for just about a minute, until fragrant. Carefully pour in the wine, scraping the brown bits on the bottom of the pan to deglaze. Allow to simmer for about 2 minutes, until the mixture reduces slightly, stirring occasionally.

Add both of the mustards to the pan. Stir to combine and allow to cook for a minute.

In a large measuring cup, combine the 2 cups of chicken stock with the 2 tbs. of flour. Whisk to combine, then pour into the pan with the mustards. Bring the mixture to a boil, then reduce the heat to low.

Nestle the chicken back into the sauce; add in the heavy cream. Cover and cook for about 10 minutes or until chicken is cooked through.

Garnish with fresh parsley.