Place an oven rack in the middle position and preheat the oven to 200°F to keep cooked chicken warm.
Set up three shallow dishes: put the all-purpose flour in the first, the beaten eggs in the second, and the Panko breadcrumbs in the third.
Pat the chicken strips dry with paper towels and season both sides with salt and freshly ground black pepper.
Working one strip at a time, dredge a chicken strip in flour, shake off excess, dip into the beaten eggs, then press into the Panko to fully coat; place on a plate and repeat with remaining strips.
Heat the oil in a 12-inch nonstick skillet over medium-high heat until it is shimmering but not smoking.
Fry half of the breaded chicken strips in the hot oil, turning as needed, until golden brown and cooked through, about 4 to 6 minutes total; transfer to a paper towel-lined plate and keep warm in the oven.
Return the skillet to medium-high heat and cook the remaining breaded chicken strips the same way until golden and cooked through, about 4 to 6 minutes.
While the chicken finishes, make the honey mustard sauce by whisking together the Dijon mustard and honey; season with salt and freshly ground black pepper to taste.
Serve the hot chicken fingers immediately with the honey mustard dipping sauce.
