Preheat oven to 325 degrees F. Make caramel by combining sugar and water in a medium saucepan and cooking over moderate heat swirling occasionally until color begins to turn golden, about 12 to 15 minutes. Turn heat to low and continue cooking and swirling constantly until color is dark brown and mixture smells of caramel. Remove from heat and pour into a 9-inch round cake pan. Using a towel or hot pad, tilt pan and swirl caramel to coat the bottom and sides well. It will need a few minutes to cool down in order for about 1/4-inch of caramel to stick to the pan. Then pour excess back into the pot it was cooked in and add 2 cups milk. Cook over low heat, stirring frequently, to dissolve excess caramel into milk, about 3 to 5 minutes. Strain warm milk and caramel mixture in a bowl and add cold half and half. Mix well. Add sugar, eggs, yolks and vanilla. Whisk custard to mix and strain into caramelized pan. Set flan into a roasting pan in the oven and pour boiling water into roasting pan until it rises halfway up the sides of the cake pan. Bake for 40 to 45 minutes or until center feels just firm when pressed gently with the fingertips. Set aside to cool for about 1 1/2 hours then cover with plastic wrap and refrigerate overnight or up to 4 days.

To serve, run a knife along the inside edge to loosen. Cover with a platter and quickly invert. Carefully drain excess caramel into a small sauce pitcher and reserve. Serve wedges of flan on dessert plates topped with extra caramel sauce.