Preheat oven to 375℉. Grease a loaf pan with olive oil or coconut oil. Set aside.
In a large mixing bowl sift together, all-purpose gluten free flour, baking soda, baking powder, cinnamon, and salt.
In another mixing bowl mash up the bananas. Mix in eggs, brown sugar, and vanilla.
Add the banana mixture to the flour mixture and mix until combined. Stir in olive oil.
Toss strawberries with 1 tablespoon all-purpose gluten free flour and then fold the strawberries into the batter.
Pour the batter into the prepared loaf pan.
Cook for 10 minutes. Reduce heat to 350℉ and continue cooking for anther 30 minutes or until a toothpick comes out clean. The top of the bread should be slightly brown.
Allow the bread to cool for one hour before slicing and serving.