01 - Season the chicken breasts generously with salt, pepper, and garlic powder on both sides, ensuring even coverage.
02 - Heat olive oil and butter in a large skillet over medium-high heat until butter foams. 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 same skillet; sauté for 2-3 minutes until softened and fragrant, being careful not to burn the garlic.
04 - Pour in chicken broth, using a wooden spoon to scrape 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 incorporate mustard.
06 - Return chicken breasts and any accumulated juices to the skillet. Simmer on low heat for 6-8 minutes until chicken is fully cooked through and sauce has thickened enough to coat the back of a spoon.
07 - Stir in lemon juice and adjust seasoning with additional salt and pepper if needed. Garnish with extra fresh dill and serve immediately.