Season chicken breasts on both sides with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Sear chicken for 5 to 7 minutes per side until the internal temperature reaches 165°F (74°C). Remove chicken from the pan and set aside.
In the same skillet over medium heat, melt the butter. Add the minced garlic and sauté for 1 minute until fragrant.
Add the white wine to the skillet, scraping the bottom with a spatula to deglaze. Simmer for 2 to 3 minutes until the liquid is reduced by half.
Reduce heat to medium-low. Whisk in the heavy cream and Dijon mustard until well combined.
Add the dried tarragon and simmer the sauce for 3 to 5 minutes until it thickens slightly.
Return the chicken breasts to the skillet, spooning the sauce over the meat to coat. Garnish with chopped parsley and serve immediately.