Add sugar and water to a saucepan. Cook over medium heat without stirring. Let the sugar melt slowly until it becomes a deep golden caramel. Carefully pour into the baking pan.

Pour the milk and heavy cream into another saucepan. Heat gently without boiling. Add chopped chocolate and whisk until smooth, creamy, and completely melted with no lumps.

Place eggs, egg yolks, sugar, vanilla, cocoa powder, and salt into a large bowl. Whisk until smooth. Slowly add the warm chocolate mixture while whisking continuously to prevent scrambling.

Pour the chocolate mixture through a fine strainer into another bowl. This removes any small egg pieces and creates a silky, smooth custard with a perfect texture.

Carefully pour the custard over the cooled caramel inside the prepared baking pan. Tap the pan gently on the counter to remove trapped air bubbles.

Place the filled pan inside a larger baking dish. Pour hot water around the pan until it reaches halfway up the sides. This helps the custard bake evenly.

Bake at 325°F (163°C) for about 60 minutes. The center should still jiggle slightly. Remove carefully from the oven and let it cool completely.

Cover the flan and refrigerate for at least six hours or overnight. Run a knife around the edges. Turn onto a serving plate before slicing and serving.