Add all of the ingredients for the apple filling except for the tapioca flour to a small saucepan. Cover, heat over medium-high heat on the stove top, and bring mixture to a full boil. Stir occasionally and allow mixture to cook at a gentle boil until the apples have leached out a great deal of liquid. 

Add the tapioca flour and continue cooking and stirring, until the mixture is very thick, about 15 to 20 minutes total. Remove from heat and set aside or refrigerate until ready to use.

While the apple filling is cooking, prepare the rest of the recipe.

Preheat the oven to 350 degrees F and line a 8” x 8” cake pan with parchment paper.

Stir together all of the ingredients in a mixing bowl. Keep stirring until a thick, moist, crumbly dough forms.

Measure out ½ cup of the crust mixture and place it in a bowl to use as the topping. 

Press the rest of the crust mixture into the parchment-lined cake pan until you have an even layer of crust. Poke several times with a fork to ensure even baking. Bake on the center rack of the preheated oven for 12 to 16 minutes, or until the crust is golden-brown and appears as though it has set up. 

Remove the crust from the oven.

Spread the apple filling mixture over the crust in an even layer. Sprinkle the reserved topping mixture over the apple layer. 

Bake the bars for 20 to 25 minutes, or until the crumb bar topping is golden-brown. Remove from the oven and allow crumb bars to cool at least 30 minutes before slicing and serving.