Preheat your oven to 350°F (175°C) to ensure it's hot and ready for baking the flan.
In a medium saucepan, combine 1 cup granulated sugar and 2 tablespoons water over medium heat. Stir to dissolve the sugar, then cook while occasionally swirling the pan until the mixture turns an amber color, being careful not to burn it. Quickly pour the caramel into a round 9-inch pan, swirling it around to coat the bottom and lower sides completely. Allow the caramel to cool and harden for about 10 minutes before adding the custard.
In a blender, add the can of evaporated milk, can of sweetened condensed milk, 5 eggs, 4 oz cream cheese (softened and cubed), 3/4 to 1 cup pumpkin puree, 2 tablespoons sugar, 1/8 teaspoon salt, 1/2 teaspoon ground cinnamon, 1 teaspoon pumpkin pie spice, and 1/2 teaspoon vanilla extract. Blend everything together until the mixture is smooth and fully combined. I find blending on high for 45 seconds helps make the custard extra creamy.
Carefully pour the blended custard mixture over the cooled caramel in the round pan. Gently place the pan into a larger baking dish to create a water bath. Fill the larger dish with hot water until it reaches halfway up the sides of the flan pan. Carefully transfer the set-up to the preheated oven and bake for 50-60 minutes, or until a fork inserted into the center comes out clean. For a silkier texture, try not to overbake.
Remove the flan pan from the water bath and allow it to cool at room temperature. Once cooled, refrigerate for 3-4 hours to let the flan set completely before unmolding and serving.