Use an electric mixer to beat the softened cream cheese until smooth. Wipe any lumps of cream cheese off of the mixer and the sides of the bowl, then add the granulated sugar, sifted cocoa powder, salt, and cornstarch, and mix until evenly combined.
Wipe the sides of the bowl, then add the room temperature sour cream, vanilla extract, and red gel coloring. Add more color if needed, and mix to combine. Make sure the cheesecake batter is completely smooth with no lumps at this point, because you want to mix as little as possible once the eggs are added.
Add the room temperature eggs, one at a time, and mix on low speed until just combined after each. Wipe the sides of the bowl with a rubber spatula and mix until the batter is smooth.
Pour the batter into the springform pan over the pre-baked crust. Bang the pan on your counter a few times to release any pockets of air.