Preheat your oven to 350°F (175°C).
Grease an 8-inch square baking dish or a similar-sized pan.
In a large bowl, whisk together the flour, light brown sugar, baking powder, baking soda, and salt.
In another bowl, mix the dairy-free yogurt, melted coconut oil, vanilla extract, and date paste until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.
Fold in the crunchy peanut butter.
Pour the batter into the prepared baking dish and spread it evenly.