Preheat the oven to 350°F. Spray a 9x5-inch loaf pan with nonstick cooking spray and set aside.
In a medium bowl, sift together 2 cups flour, baking powder, baking soda, and salt. (Don’t skip this step—it helps keep the loaf light!)
In a separate bowl, mash the bananas with a fork and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the softened butter and sugar on medium-high speed for about 2 minutes, scraping down the sides of the bowl as needed.
With the mixer on low, add the egg and mix until well combined.
Add the buttermilk and vanilla. Mix until just combined (about 1 minute).
Gradually add the flour mixture to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Remove the bowl from the mixer. Gently fold in the mashed bananas.
Before adding the strawberries, toss the diced strawberries with 1 tablespoon of flour. This helps keep them from sinking to the bottom of the loaf. Gently fold the floured strawberries into the batter.
Pour the batter into the prepared loaf pan, smoothing the top.
Bake for 80-90 minutes. If the top is browning too quickly, tent it loosely with aluminum foil. The bread is done when a toothpick inserted into the center comes out mostly clean with a few moist crumbs but no wet batter.
Let the bread cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.