Preheat the oven to 350°F / 175°C and grease a 9-inch springform pan.
Whisk together flour, cocoa powder, 1/2 cup sugar, 1 egg, oil, and red food coloring until smooth, then pour into the pan and bake for 25 minutes until a toothpick comes out clean.
Beat cream cheese, sour cream, 1/2 cup sugar, 1 egg, and vanilla until smooth, then pour over the cooled cake layer.
Bake at 325°F / 160°C for 50 minutes until the center is just set, then turn off the oven and let the cheesecake cool inside for 1 hour.
Refrigerate for at least 4 hours or overnight until fully chilled and firm.
Beat remaining cream cheese with powdered sugar until fluffy, then spread or pipe over the chilled cheesecake before slicing.