How to turn a cake recipe into a cake-cookie recipe?

I basically agree with HalfPint, as whatever we recommend here is entirely empirical and will not have been tested. But i actually love challenges like this, so if you don’t mind risking having to ditch ingredients, I’m willing to take this on. For guidance, I turned to Michael Ruhlman's wonderful book Ratio which, if this is something you like to do, is super helpful in understanding how to build recipes. According to Michael, a quick bread is (by weight) 2 parts flour, 2 parts liquid, 1 part egg and 1 part fat. (In this case, the mashed banana also serves as the liquid.) A cookie is 1 part sugar, 2 parts fat, and 3 parts flour. No liquid. There is also a wonderful book, Bakewise, by Shirley Corriher, that helps explain the science of these ingredients. It seems to me that the big issue with this recipe is going to be how to get everything to hold together. You'll know after it's mixed whether it can be scooped into cookies. To set yourself up for success, use high protein flour (bread flour if you have it). If not, you might have to add another 1/4 cup of four to your dough to make it scoopable. We're also going to let the dough sit in the refrigerator for a few hours to firm up before scooping into cookies. Here goes:
Ingredients:
300 grams (2.5 cups) flour
1/2 teaspoon baking soda
113 grams (1/2 cup or 1 stick) butter, softened to room temperature
100 grams (1/2 cup) sugar
100 grams (1/2 cup) mashed banana
1 egg
1 teaspoon vanilla extract
1 banana, sliced

1. In a large bowl, whisk together flour, baking soda and salt till thoroughly blended. Set aside.
2. Using an electric mixer with a paddle attachment on medium speed (you can do this by hand like in the recipe if you have really strong arms; a mixer is easier), mix the butter with the sugar until it lightens in color and is blended together. Blend in egg, vanilla and banana with the butter-sugar mixture until they are well blended. (Sometimes this mixture can look curdled. Don't worry about it.)
3. On slow speed, stir the flour mixture into the butter-sugar-egg mixture till just blended, scraping down the sides as needed. Make sure that everything is blended together well, and that there are no pockets of dry flour at the bottom of the bowl. If this mixture is really liquidy, add another 31 g (1/4 cup) of flour and blend well.
4. Cover the bowl and put it into the refrigerator for at least 4 hours (or overnight).
5. When you're ready to bake the cookies, heat the oven to 350 and line a cookie sheet with parchment. (Let the oven get to temperature before you take the dough out of the refrigerator.)
6. Using a cookie scoop or two tablespoons, scoop tablespoon sized balls of dough (fingers crossed) onto the cookie sheet, about 2 inches apart. (We have no idea how much these will spread.) Top each cookie dough ball with a banana slice if you want (like in the cake recipe you referred to)
7. Bake until cooked through, approximately 15 minutes (again, this is a guess), rotating the pan front to back at the 8 minute mark.
8. If the first batch spreads out into an unholy mess, butter or pan spray an 8x8 pan, scrape the rest of the dough into that, spread it evenly, top it with banana slices, and bake it off like brownies (about 30 minutes, but watch carefully). Cut into squares when cool.

Good luck! Please let us know how this turns out!

You may need to do more than scooping the batter into cookie-sized portions and shortening the bake time. You need to turn the batter into a dough that will not spread out when baked. This could mean adding more flour and/or less liquid. Rather than reinventing the wheel, try searching the internet for "banana bread cookies recipe". Lots of this recipes out there. Good luck!