Preheat the oven to 350 degrees F (175 degrees C). Grease a 10-inch fluted tube pan (such as Bundt), then lightly dust with flour; tap to remove excess.

Fill a shallow baking pan with enough water to come 1/3 up the sides of the tube pan. Place water bath in the oven to warm up while it is preheating.

Pour cajeta caramel sauce into a microwave-safe bowl. Microwave until warm and pourable, about 1 minute. Pour into the prepared tube pan, completely covering the bottom.

Whisk flour, cocoa powder, baking soda, and baking powder together in a bowl.

Beat 10 1/2 tablespoons butter in a bowl with an electric mixer until smooth. Add sugar; beat until light and fluffy. Beat in 1 egg and coffee. Add flour mixture, alternating with milk, mixing well after each addition. Pour batter over caramel in tube pan.

Combine evaporated milk, sweetened condensed milk, 4 eggs, and vanilla extract in the bowl of a food processor; pulse until smooth. Pour over cake batter through a fine-mesh sieve.

Bake in the water bath in the preheated oven until a toothpick inserted into center comes out clean, about 1 hour.

Cool on a wire rack for about 1 hour. Carefully run a thin knife around the edges to loosen, tap pan firmly a few times then shake gently. Place a serving plate over the pan and invert to release cake onto the plate.