Preheat the oven to 350°F (175°C).

In a medium heavy-bottomed saucepan combine ¾ cup sugar and ¼ cup water. Cook over medium heat, without stirring, until the mixture turns a golden amber color, gently brushing down the pan sides with a damp pastry brush or small spoonful of water if sugar crystals form. Watch closely so the sugar does not burn.

Remove the saucepan from the heat and immediately pour the hot caramel into a deep-dish pie pan or a 2‑quart round baking dish, tilting the dish to evenly coat the bottom with caramel. Be careful—caramel is very hot. Let the caramel sit and harden for 10 minutes.

Meanwhile, in a medium bowl beat 8 ounces softened cream cheese until smooth and fluffy, scraping down the bowl as needed to remove lumps.

Add 5 large eggs to the cream cheese one at a time, mixing after each addition until just combined.

Add 1 (14-ounce) can sweetened condensed milk, 1 (12-ounce) can evaporated milk, and 2 teaspoons vanilla extract to the bowl. Mix until the mixture is fully smooth and homogeneous.

Pour the cream cheese and milk mixture gently over the set caramel in the prepared baking dish.

Place the filled baking dish into a larger roasting pan or baking pan. Carefully pour boiling water into the larger pan until the water comes about 1 inch up the sides of the flan baking dish to create a water bath.

Transfer the pans to the preheated oven and bake 50–60 minutes, or until the flan’s center is set and only slightly jiggles when the dish is gently shaken.

Remove the baking dish from the water bath and place it on a wire rack to cool for 1 hour.

After cooling, cover the flan and refrigerate overnight (at least 8 hours) to fully chill and set.

To unmold, run a thin knife around the edges of the baking dish to loosen the flan, place a rimmed serving plate over the dish, and carefully invert to release the flan so the caramel runs over the top.