Cook the bacon in a skillet until crisp, then drain on paper towels. Once the bacon is cool, roughly chop it (you should have about 1/2 cup).
Combine the flour, baking soda and salt in a medium bowl. In a large bowl, beat the butter, mayonnaise and sugars with a mixer at medium speed until fluffy, about 3 minutes. Beat in the eggs, one at a time, until well blended. Add the peanut butter and vanilla and beat until combined.
At low speed, add the flour mixture in batches, beating until just combined. Using a wooden spoon, stir in the chocolate chunks, bacon, peanuts and banana chips. Cover the bowl with plastic wrap and chill for at least 30 minutes or overnight.
Position the racks in the upper and lower thirds of the oven and preheat the oven to 325 degrees F. Line 2 muffin tins with paper liners.
Fill the muffin tins about halfway full with the batter (a 2-inch, 2-ounce ice cream scoop gives you just about the perfect amount, and helps prevent spilling).
Bake until the tops are slightly golden and a toothpick inserted into the center comes out clean, about 30 minutes. (Keep in mind that the cookies won't rise and form a dome like a cupcake.) Let cool in the muffin tins on wire racks for about 10 minutes, then unmold the cookie cups and transfer them to the racks to cool completely.
The mayonnaise in this recipe makes these cookies especially tender.
Claudia Sidoti for Cooking Channel