Summarize:

Heat the sugar until it's melted and golden -- take care not to burn it. Tilt the pan to coat the bottom of the cup. Let the melted sugar stand in the cups for 10 minutes. Beat 6 eggs, 3 cups of milk, and 3/4 cup of sugar together until the ingredients are combined but not foamy.  Pour boiling water up to 1 inch (2.5 cm) in the pans. Bake them until a knife or toothpick inserted near the center comes out clean. Remove the custard cups from the pans and cool them on wire racks. Enjoy this caramel custard while it's nice and warm or chill it for a few hours before you eat it.
Preheat your oven to 350ºF (176ºC). Cook and stir 3/4 cup of sugar over low heat in a medium saucepan. Pour the melted sugar into 6-oz. custard cups. Beat the eggs, milk, vanilla extract, and the remaining sugar together in a large bowl. Pour the mixture over the caramelized sugar. Place the cups in two 8-in square baking pans. Bake the cups for 40-45 minutes. Serve. Finished.