Into a medium saucepan, sift together the cornstarch, sugar, salt, and cocoa powder. Slowly whisk in the half-and-half, until the mixture is combined and smooth. Whisk in the egg yolks, one at a time, until smooth.
Cook the pudding over medium heat, whisking continuously, until the pudding starts to thicken and large bubbles form and plop, like slowly bubbling hot lava, on the surface of the pudding. Reduce the heat to low, and continue cooking, stirring continuously for 1 minute. Check the consistency of the pudding by running your finger across the back of the stirring spoon; if it leaves a trail that does not immediately fill in, it is thick enough.
Remove from the heat and stir the vanilla, peanut butter, and chocolate chips into the hot pudding until thoroughly melted and combined.
Place eight 4-ounce custard cups or ramekins on a rimmed baking sheet. Pour the pudding into the cups, using a damp paper towel to clean up any drips. Cover the custard cups with plastic wrap. Alternatively, pour the pudding into a large bowl and cover the surface of the pudding with plastic wrap to prevent a skin from forming. Refrigerate the pudding until very cold, at least 4 hours and up to overnight.
To serve, top the custard cups with a dollop of whipped cream and a sprinkling of chocolate jimmies (also called chocolate vermicelli). If refrigerated in the larger bowl, you can scoop it into small dessert dishes or the Chocolate Balloon Cups and top with whipped cream and chocolate jimmies.