In a large mixing bowl, using an electric mixer, beat butter and sugar at medium speed until light and fluffy, about 3 to 4 minutes,
Beat in egg whites and eggs one at a time, stopping to scrape down the sides of the bowl a few times.
Add 2 teaspoons peppermint extract.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
Add flour mixture to the butter mixture alternating with 1 1/2 cups milk. (The remaining milk is for making the pudding mix.) Add flour in 3 additions and milk in 2 and beat just until combined after each addition.
Stir in melted chocolate. Spoon batter into prepared dish, spreading it evenly.
Bake for 45 to 55 minutes, or until a toothpick inserted in the middle comes out clean. If it starts getting too brown on top, cover with foil for the remainder of the baking time.
Let cake cool 10 minutes. Use the end of a wooden spoon to poke holes every 1/2-inch.
In a large bowl, whisk together the 2 pudding mixes, remaining 3 1/2 cups milk, and 1 teaspoon peppermint extract until it starts to thicken and is smooth. Don't let it thicken too much or it will not seep down into the cake.
Slowly pour pudding mixture over cake and smooth it and ease it down into the holes with a spatula.. Cover and refrigerate at least 4 hours or up to 3 days.
Spread whipped topping over cake and sprinkle with crushed peppermint candies.