Preheat oven to 350°F/180°C and have a baking tray (large enough to hold eight 4-ounce ramekins) and hot water ready.
Lightly grease the ramekins with butter or oil.
For the Caramel
Add the sugar into a saucepan and pour the water along the side of the saucepan. Add the corn syrup and let it heat gently on medium heat. Do not stir. When the sugar starts to dissolve, gently swirl it to mix the water and sugar together.
When all the sugar has dissolved, swirl the saucepan occasionally to mix the caramel. Keep an eye out for the caramel changing colour and then immediately remove from the heat when it starts to turn dark amber in colour.
Carefully pour this into the ramekins and swirl gently to spread the caramel on the bottom. Set aside.
For the Custard
Whisk the eggs, yolks and vanilla together until foamy. Add the 1 cup of cream and whisk to combine.
In a small saucepan, combine the sugar, ground coffee, 2 cups of half and half, and heat gently until the sugar completely dissolves and the milk just starts to simmer. Turn off the heat and let the coffee steep for about 10 minutes.
Strain the coffee-milk mix through a fine sieve to remove coffee grounds.
Whisk a little of this coffee-milk mixture into the cream and egg mix slowly to temper it, and then carefully add the rest to the whisked eggs. Strain the mix through a fine sieve to remove any large egg pieces.
Pour into the ramekins and place them in the baking tray. Add hot water into the tray to fill it half way up the sides of the ramekins to form a water-bath. Bake the custard in the water-bath for 25-30 minutes until the custard is done. Remove from the oven. The middle of the custard will be very slightly wobbly, but the custard will continue to cook and set as they cool down. Remove ramekins from the water-bath and let them cool down to room temperature.
Cover and chill in the fridge for at least 3-4 hours. Overnight is better.
When ready to serve, run a flat, warm knife along the sides of the custard to loosen it. Invert the coffee flan onto your serving plate.