Step 1: Grind the Flaxseed: Use a spice grinder to pulverize the flaxseed until it becomes a fine meal.
Step 2: Pour in the hot water. Stir the mixture with a fork until it thickens. Then set it aside.
Step 3: Preheat the Oven to 375°F.
Step 4: Peel the bananas and slice them into ¼-inch cross-sections. Place them on a parchment paper-lined baking sheet and place them in the freezer until they're frozen solid, which should take about an hour.
Step 5: Place the plant-based, room-temperature butter into the bowl of an electric mixer. Use the paddle attachment to beat the butter at medium speed until it's well-creamed.
Step 6: Add the peanut butter to the butter. Continue to beat at medium speed until thoroughly combined.
Step 7: At medium speed, add the sugar, vanilla, and flaxseed egg until thoroughly blended. Halfway through, scrape the sides of the bowl with a spatula to make sure all the ingredients are completely incorporated into the mixture.
Step 8: Add the baking soda, flour, and salt. Mix these in on low. Again, scrape the sides of the bowl halfway through to ensure that all the ingredients are completely combined.
Step 9: Refrigerate the dough for at least 15 minutes.
Step 10: Scoop tablespoon-sized balls of dough onto a cookie sheet lined with parchment paper. Cookies should be at least 2 inches apart.
Step 11: Take the banana slices out of the freezer. Press one slice onto each cookie. Technically, this step is optional, since you can have peanut butter cookies sans bananas. But combining these flavors results in an extra-tasty cookie, so we recommend not leaving the bananas out.
Step 12: Sprinkle a little brown sugar on top of each banana. Again, this step is optional but highly recommended.
Step 13: Bake the cookies for 12-15 minutes. When the bottoms are golden brown and the cookies can be lifted cleanly from the cookie sheet, they're done.
Step 14: Remove the baking sheet from the oven and place it on a cooling rack.