Put the flour, cayenne, salt and pepper in a wide, shallow bowl. In another wide, shallow bowl, lightly beat the eggs and 1 Tbs. of the mustard. Process the pretzels in a food processor until a coarse flour forms, about 30 - 45 seconds. Transfer the pretzel flour to a third wide, shallow bowl. Line up the flour, egg, and pretzel bowls in that order.
Put the chicken on a cutting board, and holding your knife parallel to the board, split each breast in half horizontally. You could also pound out the chicken until the chicken is thin and all the same thickness. Dredge both sides of the chicken in the flour, then the egg, and then the pretzel flour, coating well and shaking off the excess. Transfer to a baking sheet and refrigerate for 5 minutes.
Meanwhile, in a small bowl, mix the remaining 1/4 cup mustard with the mayonnaise, dill, honey, and 1/8 tsp. black pepper; set aside.
Heat the oil in a 12-inch skillet over medium-high heat. When the oil is hot but not smoking, add some of the chicken breast pieces. Don't over proud the pan. Cook until the first side is dark brown, about 3 minutes. Carefully flip and cook until the chicken is cooked through and the second side is golden-brown, about 4 minutes more; if the chicken seems to be browning too fast, reduce the heat to medium. Transfer to a cooling rack so the underside of the chicken doesn't get soggy. Repeat with the remaining chicken.
Serve with the dipping sauce.