Pulse 3 cups of the caramel corn in a food processor until finely ground. Transfer to a medium saucepan; add the milk, heavy cream, sugar and salt and stir to dissolve. Bring to a boil, then remove from the heat and let steep 30 minutes.
Whisk the egg yolks and cornstarch in a medium bowl until smooth; slowly pour in the milk-caramel corn mixture, whisking to combine. Pour the mixture back into the saucepan and cook over medium heat, stirring constantly with a wooden spoon, until the mixture coats the spoon, about 8 minutes. Strain through a fine-mesh sieve into a bowl to remove the ground caramel corn. Whisk in the butter and vanilla until smooth.
Pour the mixture into 8 small bowls. Press plastic wrap directly onto the surface of each pudding to prevent a skin from forming. Refrigerate until set, at least 4 hours. Top with the remaining caramel corn and the peanuts.