01 - Rub chicken breasts thoroughly with salt, black pepper, and garlic powder on both sides to ensure even flavor distribution.
02 - Heat olive oil and butter in a large skillet over medium-high heat. Place chicken breasts in the pan and sear for 4-5 minutes per side until golden brown and nearly cooked through. Transfer to a plate and reserve any accumulated juices.
03 - Reduce heat to medium. Add chopped shallot and minced garlic to the same skillet. Sauté for 2-3 minutes, stirring frequently, until softened and fragrant but not browned.
04 - Pour in chicken broth while scraping up any browned bits from the bottom of the skillet with a wooden spoon. Allow the mixture to simmer for 2 minutes to reduce slightly.
05 - Stir in heavy cream, Dijon mustard, and chopped fresh dill. Bring the mixture to a gentle simmer, stirring constantly to incorporate all ingredients.
06 - Return chicken breasts and any reserved juices to the skillet. Reduce heat to low and simmer for 6-8 minutes, or until chicken reaches an internal temperature of 165°F and sauce has thickened enough to coat the back of a spoon.
07 - Stir in lemon juice and taste the sauce. Adjust salt and pepper as needed. Garnish with additional fresh dill and serve immediately while hot.