Place eggs in a large saucepan and cover with cold water. Set pan over medium-high heat and bring water to a boil. Turn off heat, cover pan with a lid, and let sit for 11 minutes. Drain, rinse eggs under cold water, and peel.
Halve eggs lengthwise and scoop out yolks into a medium bowl. Add mayonnaise, hot sauce, and Dijon mustard to bowl, then mash yolks with the back of a fork and stir until mixture is smooth. Season with salt and pepper.
Spoon mixture into each egg.
Snip scallions into tiny strips and press down so that they crease at the sides. When you prop them into the filling of the egg, they look like bunny ears.