Preheat oven to 180°C (360°F) and line a baking tray with parchment paper.
In a bowl, stir the peanut butter together with the granular sweetener until creamy. Once smooth, add the oat flour (or almond flour). With the help of a fork, mix until the peanut butter cookie dough gets thicker.
Form a smooth dough and refrigerate for at least 20 minutes. This will prevent the cookies from falling apart.
After refrigerating, form some smaller balls with the dough and line over the prepared baking tray. Flatten cookies with a fork in a criss-cross pattern.
Bake in hot oven for about 10 minutes.
Before serving, let the vegan peanut butter cookies cool completely over a baking tray.