In a liquid measuring cup, stir together the milk and half and half or cream. Very slowly pour the liquids into the sugar mixture while whisking constantly. When the mixture is homogenous, turn the burner onto medium heat. When steam is rising from the top, drop the heat to medium low, then ladle some of the hot milk mixture into the beaten egg, whisking vigorously and constantly. When that ladle-ful is incorporated, whisk another in, whisking constantly again. do this once more, then pour the warm egg mixture into the hot milk/custard in the pan, whisking constantly and vigorously. Whisk constantly or stir vigorously with a wooden spoon until the mixture has thickened. Pour through a fine mesh sieve positioned over a batter bowl or large heat-proof measuring cup or bowl.