Preheat a large skillet to medium-high heat with the butter and oil. Combine the flour, reserving one tablespoon, with the cornstarch and salt. Dredge the chicken on both sides in the flour mixture.

When the butter is foamy, add the chicken to the skillet and let cook for 3 - 5 minutes on the first side until browned on the bottom and opaque at the edges. Flip, and cook for 3 minutes more until chicken is fully cooked through. Remove the chicken to plates for serving.

In the same pan, make the sauce. Reduce the heat to medium-low and sprinkle the remaining tablespoon flour over the pan drippings. Whisk to combine. Add the dijon and garlic, and whisk again to combine. Pour in ½ cup chicken stock to make a sauce, whisking until smooth. Add more stock to your preference to form a thin gravy.

Right before serving, add the capers to the sauce. Taste, and add more salt if you'd like.

Serve the chicken with pasta and arugula, drizzled with the sauce.