Let's cook.
Pat chicken breasts dry with paper towels and season lightly with salt and pepper.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add chicken breasts and sear for 4-5 minutes per side, until golden brown. Remove chicken from skillet and set aside.
Add sliced mushrooms to the same skillet and cook over medium heat for 5-7 minutes, stirring occasionally, until softened and browned. Add minced shallot and cook for another 1-2 minutes until fragrant.
Pour in the dry white wine, scraping up any browned bits from the bottom of the skillet. Bring to a simmer and cook for 2-3 minutes, allowing the wine to reduce slightly.
Stir in the heavy cream and Dijon mustard. Bring the sauce to a gentle simmer, then reduce heat to low.
Return the seared chicken breasts to the skillet, nestling them into the sauce. Cover and simmer for 8-10 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Taste the sauce and adjust seasoning with salt and pepper if needed. Garnish with fresh chopped parsley before serving.
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