Step 1

In a small bowl, whisk the sugar, cornstarch, and salt together.

Step 2

In a medium saucepan, heat the half and half over medium heat until small bubbles form and it starts to steam, about 5 minutes.
 Slowly add the sugar mixture into the hot half & half, whisking constantly. Bring to a simmer over medium heat, making sure the pudding doesn't boil.

Step 3

Cook until thickened, stirring constantly, about 4 to 6 minutes. It should coat the back of a spoon and leave a trail when you draw your finger through it.

Step 4

Remove the pudding from the heat and whisk in the vanilla extract and butter.

Step 5

Strain the pudding through a fine mesh strainer into a clean bowl. Put the bowl in an ice bath (½ ice and ½ water). Stir occasionally until just warm, about 95 °F on an infrared temperature gun or digital thermometer.

Step 6

Place plastic wrap directly onto pudding (to prevent a skin from forming), and refrigerate until the pudding is completely chilled, about 2 to 3 hours.

Step 7

Storage instructions: Homemade pudding will keep in the refrigerator, covered with plastic wrap, for 3 to 5 days.