Make the Pudding

Whisk egg in a small bowl and set aside.

Whisk cornstarch, cocoa, milk, and Nectresse in a medium saucepan until combined. Heat over low heat, stirring constantly, until mixture thickens, about 5 minutes.

Remove from heat and pour a ladleful of the hot chocolate mixture in with the egg bowl, while whisking the egg. Pour egg mixture into hot pan and stir until combined. Return to heat and cook just until it boils. Remove from heat. Stir in butter, vanilla, and chocolate chips. Pour into a bowl and cover the top with a layer of plastic wrap to prevent skin from forming. Chill until cooled.

Make the Fudgsicles

Mix peanut butter, Nectresse, and 1/2 cup milk in a medium bowl with a hand mixer.

Stir 1/2 cup milk into the cooled chocolate pudding.

Fill the bottom third of your popsicle molds with chocolate pudding. Divide the peanut butter mixture evenly among the molds. Fill with the remaining pudding. Cover and freeze until firm, at least 6 hours.