Equipment:  skillet (not sauce pot),  8X3 round cake mold and roasting pan. 

Preheat oven to 350°.  

Add to a skillet over medium-high heat about 3/4 to 1 cup of granulated sugar.   Don't stir it, instead watch it until the edges start to turn a golden color.  Using a temperature safe spatula, begin to move the sugar around in the pan - always away from you.   As the sugar becomes caramel, it will develop that golden color.   When all the granules have dissolved and you get a glass-like sheen, turn the heat off.  

CAREFULLY, pour the hot caramel into your mold.  Wear oven mittens to protect your hands.  Rotate the pan so the sugar coats the pan.  You can also use a spatula to gently move the sugar around and coat the bottom and sides evenly.  As the caramel cools, it will harden.  Once all the sides and bottom are evenly coated, set the mold aside.  

In a separate bowl, using a hand-held mixer, cream the cream cheese.   Add eggs and egg yolks and mix to combine.  Add sweetened condensed milk, evaporated milk and vanilla.  Mix well to combine all ingredients.  

Pour the custard mixture through a sieve into the mold. 
Note: The sieve will capture any cream cheese and egg particles that didn't blend well.  This step ensures no lumps or clumps in your flan.  

Place the custard in the roasting pan in the center oven rack.  Fill the roasting pan with boiling water to reach halfway up the sides of the mold.  This is a water bath or bain-marie.  

Note:  Some people place a wet dishcloth between the mold and the roasting pan.  

Bake in the preheated oven for 50 minutes to an hour.   Check for doneness.  The center should jiggle, but not separate.  If it splits, cook for 5 minutes and recheck.  

Remove the flan from the oven and allow it to cool on a baking wire rack for one hour, then refrigerate for at least 4 hours.   Leave the roasting pan in the oven and remove/discard water when it has cooled completely.  

When you're ready to serve, you need to loosen up the flan from mold.   You  need to apply a little warmth to release the bottom.  Return the mold to the roasting pan and add boiling water to the roasting pan.  As the sugar warms up again, it releases the flan from the mold.   You can also run a knife around the inside to release the sides.  

When the flan has loosened completely, place your serving dish over the flan.  Grasp both tightly with your hands and quickly flip the flan onto the serving dish.   The flan will drop onto the serving dish and the caramel sauce will spread out onto the serving dish.    Serve immediately.