Pour 1/2 cup sugar into a 9-inch round cake pan. Cook over medium heat until the sugar melts and turns light brown. Shake the pan using oven mitts to distribute the sugar evenly in the pan, but don't worry if all the sugar doesn't melt. Remove from heat and set aside to cool. You will hear it crack as it cools. That's totally normal.
In a small pot, heat the milk and remaining sugar over medium heat. Stir frequently. When the mixture is hot and frothy, turn off the heat.
Using a stand mixer or electric mixer, blend the remaining ingredients. Slowly add the hot milk using a low speed. When it's well blended, pour the mixture over the now-cooled caramelized sugar.
Wash the pot you just used and refill it with water. Heat the water over high heat until it just begins to boil.
Place the cake pan into a roasting pan. When the water is very hot, pour it into the roasting pan about an inch deep. Put the whole thing in the oven and bake for 60-70 minutes, until a cake tester stuck in the center comes out clean. The flan will still be jiggly at this point, so don't mistake its being jiggly as a sign that it's not done.
Remove cake pan from water and set it to cool on a wire rack. When it's no longer warm, cover and chill.
To serve, loosen edges and invert onto a serving platter. All of the wonderful syrup from the bottom of the pan will pour out overtop of the flan.