This is not an entirely unique recipe. I think there are a number of variants of it out there. I got my original recipe from The Gluten-Free Bible (bad name, good book). When I wanted to use fake sugar instead of the real stuff though, I found it changed the consistency and I also had to add something else. Peanut flour seemed like an easy answer. If you are not familiar with defatted peanut flour, it is wonderful stuff. I buy it online and use it in many things. It is good stirred into yogurt. If you are on the Trim Healthy Mama diet, this is an S snack. If you are counting carbs, the cookies work out to about 3g of carbs each. If you want to substitute almond butter or another nut butter, I would try using blanched almond meal for the peanut flour and see how that works (and let me know how it turns out if you do). Using xylitol keeps these low-carb. I think it gives them a cool (temperature-wise) taste.
Peanut Butter Cookies
1 c natural peanut butter
1 c xylitol
approx. 1/4 c defatted peanut flour
Preheat oven to 375. Combine peanut butter, xylitol, and egg. Gradually stir in peanut flour until mixture becomes less sticky.
Drop by spoonfuls on cookie sheet. bake approx. 15 minutes.
I found they took longer than I expected so you might want to check them after 10 minutes and then every few minutes after that. When done they will still be soft but not sticky or moist. Allow them to sit on the cookie sheet for 10 minutes or more after baking and they will firm up.