Prepare a 9x13 inch baking dish by sifting 2 cups powdered sugar evenly over the bottom of the pan. Set aside.
In the bowl of an electric mixer, sprinkle gelatin over ½ cup water. Let bloom.
In a 2-quart saucepan, combine sugar, corn syrup, and remaining ½ cup water. Stir to dissolve and bring to a boil, stirring to ensure no scorching. Bring mixture to 240°F.
Remove from heat and pour into a 2-cup heatproof glass measuring cup.
Pour a small amount of liquid on prepared gelatin and mix it on medium speed.
With the mixer running, continue to drizzle in liquid down the side of the bowl, making sure to not pour directly on the beater. Once all liquid is added, turn the mixer on high and beat until the mixture is cooled, fluffy, and has grown in volume, 8-10 minutes.
Add vanilla bean seeds and peppermint extract. Beat 20 seconds.
Pour mixture into prepared pan, smoothing out the top into an even layer.
Sprinkle with crushed candy and sift an additional 2 cups powdered sugar over the top.
Let cool 4-6 hours or overnight.
Cut and dip sliced edges in powdered sugar to ensure the squares won't stick to each other.