Cut each chicken breast in half lengthwise, then place between a folded over piece of plastic wrap. Use the flat side of a meat mallet to pound the chicken to a thickness of about ½-inch.
While you dredge the chicken, heat enough neutral oil in a large skillet over medium-high heat so that it comes up about ¼-½-inch.
Set up a dredging station with 3 shallow bowls. In the first bowl, combine flour and Kosher salt. In the second, whisk together eggs with Dijon mustard. In the final bowl, mix together breadcrumbs, panko, and sesame seeds. Dredge each chicken cutlet first in the seasoned flour mixture. Dip in the egg. Transfer to the breadcrumb bowl.
Cook until crispy on the first side, then carefully flip and cook. Transfer cooked schnitzel to a paper towel lined wire rack, then immediately sprinkle with a little Kosher salt. Repeat with remaining chicken cutlets, adding more oil to the pan as needed. Serve immediately!