Whisk together 1/2 cup mayonnaise, 2 tablespoons Dijon mustard, and 2 tablespoons maple syrup in a small bowl; season with salt and pepper to taste and refrigerate until needed.
Slice each chicken breast lengthwise into 4–5 strips and season the strips lightly with salt and pepper.
Pulse 1 1/2 cups panko, 1 cup honey roasted peanuts, and a heaping 1/4 teaspoon cayenne pepper in a food processor until finely ground; transfer to a shallow bowl or pie pan.
Place 3/4 cup all-purpose flour in a second shallow bowl and season generously with salt and pepper.
Place the 3 lightly beaten large eggs in a third shallow bowl.
Working one piece at a time, dredge a chicken strip in the seasoned flour, shake off excess, dip into the beaten eggs, then press into the peanut–panko mixture to coat thoroughly; place coated strips on a baking sheet. Repeat with remaining strips.
Preheat the oven to 350°F (175°C) and line a baking sheet for the fried strips to rest on.
Pour enough vegetable oil into a Dutch oven to reach 1–2 inches deep and heat to 375°F (190°C) using a deep-frying thermometer.
Fry the chicken strips in batches until golden brown, about 3 minutes per side; remove with tongs or a slotted spoon and transfer to the baking sheet.
Bake the fried strips in the preheated oven for 10–15 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Serve the chicken fingers warm with the chilled mayonnaise–Dijon–maple dipping sauce.
