Preheat oven to 375F.
Peel the bananas and cut to ¼-inch cross-sections.
Place them in a single layer on a sheet pan lined with parchment paper. Transfer to freezer until bananas are frozen solid, at least an hour. Set aside. Store unused bananas in a closed container in the freezer.
Add the room temperature plant-based butter to the bowl of an electric stand mixer.
Beat with the paddle attachment on medium speed until creamed.
Add peanut butter. Mix on medium until blended with the butter.
Add the sugar, flax seed egg, and vanilla extract.
Mix on medium until ingredients are evenly incorporated, scraping down the sides of the bowl with a rubber spatula halfway through.
Add the flour, baking soda, and salt.
Mix on low just until all ingredients are evenly incorporated, scraping down the sides of the bowl with a rubber spatula halfway through.
Refrigerate the dough 15 minutes.
Using a tablespoon-size scoop, scoop balls of dough onto a cookie sheet lined with parchment paper, spacing them at least 2 inches apart.
Press one frozen banana slice onto each cookie (optional but highly recommended).
Sprinkle a pinch of brown sugar on top of banana (optional but recommended).
Bake 12-15 minutes. They’re done when the cookies lift cleanly from the sheet pan and the bottoms are golden brown.
Remove sheet pan from the oven.
Place on cooling rack and allow to cool to room temperature.
To store leftover cookies, place them inside a double layer of sealed plastic bags.
To thaw frozen cookies, remove from plastic bags, and let sit at room temperature about 30 minutes.