Preheat the oven to 350 F. Combine all of the dry ingredients (oats through salt) in a large bowl. Stir to combine.
Mash the defrosted bananas and mix in the tahini and vanilla. Pour the liquid ingredients into the dry and mix well. It may seem too dry at first. Keep mixing. Switch to squishing everything together with your hands if needed.
Line an 8x11 or similar size casserole dish with parchment paper. Press the mixture into the dish. Smooth out the top and press firmly to all edges. Use a spatula or dough scraper to cut into 12 bars.
Pull the parchment paper and bars from the dish and move to a baking sheet. Pressing and cutting in a dish helps the bars keep their shape, and baking on a sheet helps them cook more consistently.
Bake for 20 minutes. They should be slightly soft to the touch - they will firm up when cool. Move the parchment paper and bars to a cooling rack and allow to cool completely before separating. Store covered in the refrigerator for one week.
Notes
* Frozen bananas partially melt into a liquid when defrosted. Using fresh mashed bananas may result in drier bars.