Preheat the oven to 350 degrees F (175 degrees C).
Mix flour, butter, and powdered sugar for crust until smooth. Pat into the bottom of an 8-inch square baking pan.
Bake in the preheated oven for 25 minutes.
While the crust is baking, prepare topping: Mix pecans, brown and white sugars, flour, eggs, vanilla, baking powder, and salt in a bowl until well combined. Fold in mulberries.
Remove crust from the oven. Spread topping over the crust and bake for another 25 minutes.
Let cool for 15 to 20 minutes before cutting into 12 bars.