Begin by seasoning your chicken breasts generously with salt, pepper, thyme, and tarragon. Heat olive oil in a large skillet over medium-high heat. Once hot, add the chicken and sear until golden brown, about 5–6 minutes per side. This step locks in the juices. Once done, remove the chicken from the skillet and set aside.
Using the same skillet with those yummy browned bits from the chicken, add the chopped onion. Cook over medium heat until soft and translucent, about 4–5 minutes. Add the minced garlic and sauté for another minute. The aroma at this stage is unbelievably tempting!
Pour in the white wine, using a wooden spoon to scrape up all the delicious bits stuck to the bottom of the pan. Bring the wine to a gentle simmer and allow it to reduce by half. This step intensifies the flavor base of the sauce.
Add the chicken broth and heavy cream, stirring to combine. Whisk in the Dijon mustard, thyme, and tarragon. Continue simmering gently until the sauce thickens enough to coat the back of a spoon.
Nestle the seared chicken back into the skillet, spooning sauce over each piece. Cover the pan, reduce heat to low, and simmer for 15–20 minutes. This gentle cooking allows the chicken to absorb the flavors while staying tender.
Sprinkle freshly chopped parsley over the finished dish for a pop of color and a fresh note. Serve hot with a generous pour of that luxurious sauce over each piece of chicken.