Preheat an oven to 300 degrees F (150 degrees C). Grease a 9x13-inch baking dish. Whisk the cocoa powder, sugar, flour, 1/4 teaspoon salt, and pudding mix together in a bowl.
Beat the eggs in a mixing bowl, then whisk in 1/2 cup margarine, 1/4 cup milk, applesauce, and 2 teaspoons vanilla extract. Stir in the flour mixture until no dry lumps remain, then spread into prepared pan. In a separate bowl, stir together the peanut butter, 2 tablespoons margarine, 1/4 cup milk, 1/2 teaspoon vanilla extract, and 1/4 teaspoon salt. Drop tablespoon-sized pieces of the peanut mixture over the brownie batter. Use a knife to run through the peanut butter to create a marbled effect.
Bake in the preheated oven until the top is dry and the edges have started to pull away from the sides of the pan, about 30 minutes. Cool to room temperature before cutting into squares.