Season both sides of the chicken liberally with the kosher salt and black pepper.
Heat a large skillet over medium-high heat. Add the olive oil (2 tablespoons) and swirl to coat. Add the chicken and cook for 5-6 minutes on each side, until browned on the outside and fully cooked through. Remove the chicken to a plate.
Add the chicken broth (1 cup) to the skillet, scraping any stuck-on bits up from the bottom of the pan with a wooden spoon. Continue heating over medium-high heat until the liquid has reduced by about half (about 5 minutes)
Add the butter (2 tablespoons), whole grain mustard (2 tablespoons), dijon mustard (2 tablespoons), and honey (2 tablespoons) to the skillet. Continue heating and stirring until butter has melted and honey and mustards have fully incorporated into the sauce.
Add the chicken back into the skillet, spooning some of the sauce on top, and heat for another minutes or so.
Serve the chicken with the sauce on top.
You can usually buy chicken breast cutlets at your store, but if you prefer, you can cut a whole breast in half horizontally to make them.
You can use another kind of chicken cut, such as thighs (boneless or bone-in, skin on) or whole breasts. Keep in mind, thighs can take a little longer to cook because they are dark meat, and whole breasts will also take longer because they are thicker. If you use whole breasts, I recommend either pounding them to a uniform, thinner thickness so they cook evenly, or you can sear them for 3-4 minutes on each side, then turn down the heat, add a little chicken broth, and cover them to finish cooking, in order to keep them more juicy and not overcooked. If you do bone-in, skin on thighs, finish cooking them in the oven after searing them skin-side down before making the sauce.
For a dairy-free or paleo version, omit the butter or use ghee instead.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.