01 - Season both sides of the chicken breasts thoroughly with salt, pepper, and garlic powder, ensuring even coverage.
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 and set aside on a plate, reserving any juices.
03 - Reduce heat to medium. Add chopped shallot and garlic to the skillet; sauté for 2-3 minutes until softened and fragrant, being careful not to burn the garlic.
04 - Pour in chicken broth, scraping up any browned bits from the bottom of the skillet. Let simmer for 2 minutes to reduce slightly.
05 - Stir in heavy cream, Dijon mustard, and chopped dill. Bring 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 cooked through (internal temperature reaches 165°F) and sauce has thickened.
07 - Stir in lemon juice and taste the sauce. Adjust salt and pepper as needed. Garnish with additional fresh dill and serve immediately.