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

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.

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.