Step 1

Whisk ¼ cup milk and cornstarch in a small bowl. Set next to the stove.

Step 2

Combine the remaining 1¼ cups milk, half-and-half, sugar and salt in a medium saucepan. Cook over medium-high heat, whisking occasionally, until bubbles start to form around the edges, about 3 minutes. Whisk the cornstarch mixture. Then, while continuously whisking the milk mixture in the pan, slowly add the cornstarch mixture. Cook, whisking constantly, until the mixture starts to thicken, about 30 seconds. Reduce heat to maintain a low simmer and cook, stirring, until very thick, about 2 minutes. Remove from heat and stir in vanilla and chocolate chips (if using).

Step 3

Transfer the pudding to a heatproof bowl. Place a piece of plastic wrap directly on the surface to keep a skin from forming. Refrigerate until cold, at least 4 hours and up to 3 days.