Set a fine-mesh sieve over a medium bowl and place it near your stove.  , In a large saucepan, whisk together the cornstarch, sugar, and salt. Add the egg yolks and whisk until fully combined, making sure to reach the edges of the pan. , Pour in the milk and heavy cream, then whisk thoroughly to eliminate as many lumps as possible.  , Set the saucepan over medium-low heat and cook, whisking frequently, for 8 to 10 minutes, until the mixture is thick enough that your whisk leaves lines in the bottom. Stir constantly toward the end, switching to a flexible spatula if necessary to reach into the edges of the pan. , Remove the saucepan from the heat, whisk in the sweetened condensed milk, and stir until the pudding is smooth and shiny. Immediately press the pudding through the sieve to remove any lumps. Whisk in the vanilla. , Transfer the vanilla pudding to a serving bowl or portion into individual ramekins or small cups or jars. Enjoy warm, or press a piece of plastic wrap or parchment onto the surface of the pudding to prevent a skin from forming and then chill until set, about 3 hours. Serve with whipped cream or berries, if desired., Store the vanilla pudding in the refrigerator for up to 5 days.