Coconut Cheese Flan (Flan de Coco y Queso)

Preheat the oven to 350 degrees F (175 degrees C).

Cook and stir sugar with a wooden spoon in a heavy skillet over medium-low heat until melted and golden, about 10 minutes. Very carefully pour hot caramel into a 9-inch round, 3-inch deep baking dish. Swirl dish to cover bottom and sides. The caramel will harden as it cools.

Combine eggs, cream cheese, and sweetened condensed milk in a blender. Cover, and blend on high until well combined; transfer to a large bowl. Pour cream of coconut, coconut milk, evaporated milk, coconut-flavored rum, and vanilla extract into the blender; cover and blend on high until well combined. Pour into the bowl with the cream cheese mixture. Whisk until incorporated. Pour the flan mixture into the caramel-coated baking dish.

Line a roasting pan with a damp kitchen towel. Place the filled baking dish on the towel, and place roasting pan in the preheated oven. Fill roasting pan with boiling water to reach halfway up the sides of the baking dish. Bake until the flan is set and a knife inserted in the center comes out clean, about 1 hour. Transfer to a wire rack; cool. Refrigerate flan until ready to serve.

To serve, run a knife around the edges of the pan and flip the flan out onto a serving platter. Spoon any caramel remaining in the baking dish over the flan.