Preheat the oven to 325°F and wrap the outside of a 9-inch springform pan tightly with two layers of foil. In a bowl, stir together the gluten free chocolate cookie crumbs, melted butter, and sugar until evenly combined.
Press the mixture firmly into the bottom of the pan. Bake for 10 minutes, then set aside to cool. In a large bowl, beat the cream cheese and sugar with an electric mixer on medium speed until completely smooth and fluffy, about 4 minutes. Scrape down the bowl thoroughly.
Sift the cornstarch and cocoa powder together, then add them to the cream cheese mixture along with the vanilla extract. Beat on low until combined. Add the red food coloring and mix until the color is vibrant and even throughout the batter.
Add the eggs one at a time, beating on low speed after each addition just until the streak of yolk disappears. Gently fold in the sour cream by hand with a spatula until the batter is smooth and uniform.
Pour the filling over the cooled crust. Place the springform pan inside a roasting pan and pour in hot water until it reaches halfway up the sides. Bake for 60 to 65 minutes, until the edges look set and the center still wobbles gently when you tap the pan.
Turn off the oven, crack the door open a few inches, and let the cheesecake cool inside for 1 hour. Then remove it from the water bath, take off the foil, and refrigerate for at least 6 hours or overnight.
For the frosting, beat the softened cream cheese and butter together until fluffy. Add the powdered sugar and vanilla, and beat on low then increase to medium until smooth and creamy.
Spread the frosting in a thick, even layer over the top of the chilled cheesecake. If desired, sprinkle gluten free red velvet cake crumbs around the edges for garnish. Slice and serve cold.