Preheat oven to 350 degrees F. Line and grease a 9 in x 5 in loaf tin. I line mine with parchment paper and grease it with an olive oil spray. Put the oven rack in the middle of the oven.
In a large bowl add 1/2 cup greek yogurt, 1/2 cup olive oil, 2 eggs, 3 mashed bananas, 3/4 cup sugar, and 2 teaspoons vanilla. Mix until everything is blended together.
In another large bowl, add 1 3/4 cups flour, 1 teaspoon baking soda, and 1/2 teaspoon salt. Mix with a fork.
Pour the bowl of dry ingredients into the bowl of wet ingredients and mix until banana bread batter forms.
In a small bowl, add the chopped strawberries and sprinkle with 1 Tablespoon of flour. Mix until all the strawberries are covered in flour.
Fold the floured-covered strawberries into the batter.
Pour the banana bread batter into the lined loaf tin. Bake for 50-60 minutes, or until a knife or tooth pick comes out clean.