Place the gelatin in the bottom of the bowl of a stand mixer. Add ½ cup cold water and set aside.
In a medium-sized pan set over a high heat, heat the sugar, corn syrup, salt, and vanilla, stirring occasionally. When the mixture comes to a full rolling boil, stop stirring, and instead swirl the pan occasionally by the handle. Attach a candy thermometer to the pot and let the mixture heat to 240 degrees F. This will take just over 5 minutes.
Using the whisk attachment of your stand mixer, turn the mixer on to medium speed and gradually pour the hot syrup into the bowl. When all the syrup has been added, pour in another ½ cup of water.
Increase the speed to high and beat for 15 minutes, until the marshmallows are thick and fairly stiff.
Divide your marshmallow mixture into as many parts as the number of colors you want to use. Beat in the food coloring, adding as little or as much as you want, depending on whether you want the marshmallows to be pastel-colored or really bright.
Grease your fingers and spoons, and transfer the marshmallow mixture into the prepared pans.
Let the marshmallows set for at least 4 hours, or overnight.
When set, turn out the marshmallow blocks onto a flat surface. Gather together the cookie cutters you will use.
Combine the cornstarch and powdered sugar. Cover the cookie cutters in this mixture in between every cut out, until all the marshmallows have been cut.
Dip your finger into a little water and coat the marshmallow in water. Dip all sides of the marshmallow in the sanding sugar until it’s completely covered. Let dry on a cooling rack.
To make the eyes on your Peeps, dab some corn syrup on to the marshmallow where the eyes will be, and, using a toothpick, add on the sesame seeds.