Prep your oven and pan. Position a rack in the center of the oven and preheat to 400°F. Line a mini muffin tin with paper liners.
Make the muffins. In a medium bowl, use a fork to mash the bananas, adding the sour cream and vanilla and stirring them into the mixture as you do. The mixture will be thick and chunky, but that's totally okay, I promise!
In another medium bowl, whisk together the flour, baking soda, baking powder, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar. Beat on medium until light, fluffy, and doubled in volume, 2 to 3 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low and add the egg, mixing until combined. Scrape down the bottom and sides of the bowl. With the mixer on low, add the dry ingredients in two equal parts, adding the second half only when the first half has been just combined. Add the banana mixture all at once and beat on low until just combined. Add the mini chocolate chips and beat until evenly distributed. Scrape down the bottom and sides of the bowl once more, and beat on low for an additional 30 seconds.
Carefully scoop a scant 1 ½ tablespoons of batter into each paper liner. Sprinkle the top of each muffin with mini chocolate chips.
Bake the muffins. Bake for 15 minutes, or until the muffins are domed and golden brown around the edges and a skewer inserted into the center of a muffin comes out with a few crumbs attached. Cool completely in the muffin tin on a wire rack.
Serve and store. Serve warm or at room temperature. The muffins can be stored under a cake dome (or a large bowl turned upside down) at room temperature for up to 3 days.