Preheat oven to 375 degrees F (190 degrees C). Coat an 8-inch pie pan with cooking spray.
Bring water and brown rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 45 to 50 minutes.
Stir peanut butter, applesauce, honey, and egg together in a bowl; add rice, garbanzo bean flour, oats, currants, coconut, sunflower seeds, chia seeds, baking powder, and ground cinnamon and stir until combined. Spread dough evenly in prepared pie pan.
Bake in preheated oven until edges are golden brown, about 20 minutes.