Season the chicken breasts with salt and pepper. In a large skillet, heat the olive oil over medium high heat. Add the chicken breasts and sauté until done, about 4 to 5 minute on each side. Remove the chicken breasts to a plate and set aside. Do not wipe out the skillet!
Add the shallot to the skillet and sauté over medium high heat for 3 to 4 minutes until tender. Add the white wine and stir to scrape up all the little flavorful bits that may be stuck to the bottom of the skillet. Simmer for about 2 minutes until the wine reduces by half. Add in the broth, and return to a simmer, stirring occasionally for another 4 minutes until the mixture reduces slightly. Add the mustard, arugula, cream and butter, and stir until the butter is melted and arugula is wilted.
Pour the sauce over the chicken breasts.
Notes
How to Make Thin-Sliced Chicken Cutlets
Rest one hand on the top of the chicken breast to hold it steady, and carefully slice the chicken breast horizontally. Each chicken breast will yield between 2 and 4 slices, depending on how thick it is. Slice carefully but decisively. You need a good, sharp knife for this to work.