Whisk together 1/2 cup mayonnaise, 2 tablespoons Dijon mustard, and 2 tablespoons maple syrup in a small bowl; season with salt and pepper and refrigerate until needed.
Slice each chicken breast lengthwise into 4–5 strips and season all over with salt and pepper.
In a food processor, pulse 1 cup honey roasted peanuts, 1 1/2 cups panko, and 1/4 teaspoon cayenne until finely ground; transfer to a shallow bowl.
Place 3/4 cup all-purpose flour in a separate shallow bowl and season generously with salt and pepper.
Beat 3 large eggs in another shallow bowl.
Working with one strip at a time, dredge chicken in seasoned flour, dip into beaten eggs, then press into the peanut-panko mixture to coat thoroughly; transfer coated strips to a baking sheet.
Preheat oven to 350°F (175°C).
Pour 1–2 inches of vegetable oil into a Dutch oven 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; use a slotted tool to transfer strips back to the baking sheet.
Bake the fried chicken strips in the preheated oven for 10–15 minutes, or until cooked through and internal temperature reaches 165°F (74°C).
Serve the chicken fingers with the refrigerated mayo–Dijon–maple dipping sauce.