Preheat oven to 300°F. In a pan over medium heat, add sugar and let it begin to caramelize before stirring until smooth. Pour the caramelized sugar into a baking pan, tilting to spread evenly, then place the pan in the freezer while you make the flan mixture.
In a blender, lightly pulse the eggs, yolks, and dulce de leche without creating too many bubbles. In a large bowl, mix heavy cream, evaporated milk, condensed milk, vanilla, and the egg mixture, being careful not to create air pockets. Strain 3 times until smooth.
Remove the caramelized pan from the freezer and place in a large baking dish. Pour the flan mixture into the pan. Add hot water to the baking dish to come halfway up the sides of the flan pan.
Bake for 1 hour and 30 minutes. Remove from oven and water bath, and let the flan rest at room temperature for 1 hour. Cover and refrigerate overnight.
The next day, run a knife along the edges of the pan. Place a plate over the pan, flip, and gently shake to release the flan. Slice and serve, buen provecho!