Preheat your oven to 400 F (205 C).
Add 2 tablespoons of butter to a large pan over medium heat. When the butter is melted and bubbly, add panko breadcrumbs and season with salt and black pepper. Cook, stirring often until panko starts to look golden brown and toasty—7 to 10 minutes.
Remove the breadcrumbs from the pan to a large plate to cool while you get the rest of your ingredients together.
Add cornstarch to another large plate.
On a third large plate, add one egg, 1 tablespoon of mayonnaise, and hot sauce. Whisk thoroughly to combine. These three plates are your dredging station.
First, each shrimp goes into the cornstarch and gets fully coated. Then each shrimp goes into the egg/mayonnaise mixture and gets fully coated again. Finally, the shrimp is dredged through the Panko breadcrumbs until they are fully coated with breadcrumbs.
Move each breadcrumb-coated shrimp to a sheet pan and bake for 7 to 8 minutes.
Serve shrimp with cocktail or tartar sauce.