Preheat the oven to 350 degrees F (180 degrees C). Grease two 9-inch round cake pans and line the bottoms with parchment paper.

Make the cake: Whisk flour, baking powder, cinnamon, baking soda, nutmeg, and ginger together in a bowl. Mix ketchup, water, and food coloring together in a separate bowl.

Beat butter in a large bowl with an electric mixer until smooth. Blend in sugar until creamy, then mix in eggs, one at a time, until incorporated. Add flour mixture in two batches on low speed, alternating with ketchup mixture, scraping down the bowl as needed, until well combined. Increase the speed to medium-high and beat for 1 minute. Divide batter evenly between the prepared pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool in the pans on a wire rack for 15 minutes, then run a table knife around the edges to loosen. Invert each layer carefully onto the wire rack. Let cool completely, about 15 more minutes.

While the cake layers are cooling, make the frosting: Beat cream cheese, butter, and vanilla in a mixing bowl with an electric mixer on medium speed until smooth, about 2 minutes. Gradually mix in powdered sugar on low speed, scraping the bowl as needed, then beat on high speed until fluffy.

Place one cooled cake layer onto a serving plate. Cover with frosting and spread to the edges. Place remaining cake layer on top. Frost the sides of the cake, then finish by frosting the top.