Pat chicken thighs dry and season liberally with salt and pepper on both sides.
Heat oil in a large cast-iron skillet over medium-high heat until shimmering.
Place chicken skin-side down in the skillet and sear until the skin is golden brown and crispy, approximately 8 to 10 minutes.
Flip the chicken and continue cooking for 5 to 7 minutes until the internal temperature reaches 165 degrees Fahrenheit. Remove chicken from skillet and set aside.
Reduce heat to medium, add garlic cloves to the rendered fat, and sauté for 2 minutes until fragrant and lightly browned.
Deglaze the pan with chicken stock, scraping the browned bits from the bottom of the skillet.
Whisk in heavy cream and Dijon mustard; simmer for 3 to 5 minutes until the sauce reduces and thickens slightly.
Stir in lemon juice and fresh parsley.
Return the chicken to the skillet, skin-side up, and spoon the sauce around the pieces before serving.