01 - Season both sides of each chicken breast thoroughly with salt, black pepper, and garlic powder.
02 - Heat olive oil and butter in a large skillet over medium-high heat. Add chicken breasts and sear for 4-5 minutes per side until golden brown and nearly cooked through. Remove chicken from skillet and set aside on a plate, reserving any juices.
03 - Reduce heat to medium. Add chopped shallot and garlic to the same skillet; sauté for 2-3 minutes until softened and fragrant.
04 - Pour in chicken broth, scraping up any browned bits from the bottom of the skillet. Simmer for 2 minutes to reduce slightly.
05 - Stir in heavy cream, Dijon mustard, and chopped fresh dill. Bring mixture to a gentle simmer, stirring constantly to combine flavors.
06 - Return chicken breasts and any accumulated juices to the skillet. Simmer on low heat for 6-8 minutes until chicken is completely cooked through and sauce has thickened to desired consistency.
07 - Stir in lemon juice and taste the sauce. Adjust seasoning with additional salt or pepper if needed.
08 - Transfer chicken and sauce to serving plates. Garnish with additional fresh dill and serve immediately while hot.