Flatten the chicken breasts/cutlets so they’re of an even thickness. You can use a meat mallet or a rolling pin. Trim any excess fat with a knife or kitchen scissors.
Season the chicken cutlets with a pinch of salt and pepper, and dredge them through the flour.
To a frying pan over medium-high heat, add the oil. Once shimmering, add the chicken to the pan (laying it away from you so the oil doesn’t splash). Cook for 3-4 minutes on the first side until golden. Then flip them and continue cooking them for another 3-4 minutes until almost cooked through. Remove them to a hot plate and cover them to keep them warm.
Add half the butter to the pan along with the minced shallot. Sauté, stirring frequently so the shallots don’t burn (for about 1-2 minutes). Add the minced garlic and lemon zest, and sauté for about 30 seconds.
Add the chicken stock and deglaze the pan, scraping up any brown bits. If you’re using a non-stick pan, don’t use metal utensils to scrape (use a heatproof silicone spatula instead). Bring to a boil, reduce the heat to a simmer, and cook for about 3 minutes. Add the cream, mustard, and honey, and stir to combine well.
Add the chicken back to the sauce and simmer for 2-3 minutes, turning the chicken halfway through. Add a teaspoon of lemon juice and the remaining butter, stirring it into the sauce until melted and well-combined. The sauce should be glossy and lightly thickened, coating the back of a spoon. Taste the sauce and adjust the seasoning, adding more salt and pepper if needed. If using a thermometer, the chicken should reach an internal temperature of 165°F (74°C) in the thickest part.
Serve the chicken while warm with mashed potatoes or another side of your choice. Optionally, garnish the chicken and sauce with some minced fresh parsley.
