Preheat oven to 300° Fahrenheit. Cut figs in half lengthwise and evenly place on the bottom of a 9 inch cake pan.
In a pan over medium heat, add sugar and water and let it caramelize without stirring. Pour the caramelized sugar over the figs, tilting to spread evenly, then place the pan in the freezer while you make the flan mixture.
In a blender, lightly pulse the eggs and yolks 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!