01 - Rub both sides of each chicken breast thoroughly with salt, black pepper, and garlic powder, ensuring even coverage.
02 - Heat olive oil and butter in a large skillet over medium-high heat until shimmering. Add chicken breasts and sear for 4-5 minutes per side until golden brown and nearly cooked through. Transfer chicken to a plate and reserve.
03 - Reduce heat to medium. Add chopped shallot and minced garlic to the skillet; sauté for 2-3 minutes until softened and fragrant, being careful not to burn the garlic.
04 - Pour chicken broth into the skillet, scraping up any browned bits from the bottom with a wooden spoon. Allow to 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 accumulated juices to the skillet. Simmer on low heat for 6-8 minutes until chicken is fully cooked (internal temperature reaches 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 if necessary. Remove from heat.
08 - Plate chicken breasts with generous sauce. Garnish with additional fresh dill and serve immediately while hot.