Vanilla pudding II

Here's another vanilla pudding recipe I tried, as part of my ongoing effort to use up milk. It had more steps than 'vanilla pudding I' and the texture wasn't as good: it was a lot runnier, it was only slightly thicker than milk. I think I didn't cook it long enough at the end - with pudding I, cooking an extra five minutes is what thickened it up. I may try this again, and cook it longer, and see how it turns out.

3 1/2 cups milk
1/3 cup plus 3 tablespoons granulated white sugar
1/4 cup cornstarch
1/8 teaspoon salt
2 large eggs
1 large egg yolk
2 teaspoons pure vanilla bean paste or pure vanilla extract
1 tablespoon unsalted butter

In a large stainless steel (or heatproof) bowl whisk together 1/3 cup sugar, cornstarch, salt, eggs, and egg yolk. Whisk in 1/2 cup of the milk. Set aside while you heat the rest of the milk and sugar. Have ready a fine medium-sized strainer and bowl as you will need to strain the pudding after it is cooked.

First, rinse a medium-sized heavy saucepan with cold water and then shake out the excess water. Then pour the remaining 3 cups of milk, along with the remaining 3 tablespoons of sugar, into the saucepan and bring just to a boil. Remove from heat and gradually pour the hot milk into the egg mixture, whisking constantly, until the mixture is smooth.

Transfer the pudding mixture to a clean, large heavy bottomed saucepan and place over medium-low heat. Cook, stirring constantly, until the mixture thickens to the consistency of mayonnaise (about 6 minutes). Remove from heat and whisk in the butter and vanilla extract. If necessary, pour through the strainer to remove any lumps that may have formed during cooking.

Pour the pudding into six or eight serving dishes, cover with plastic wrap, and refrigerate until well chilled, about two hours.

Serve cold or at room temperature.