Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan with butter or non-stick spray, then line with parchment paper, leaving overhang on two sides for easy removal.
In a medium bowl, whisk together 1 ½ cups flour, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 2-3 minutes. Add eggs one at a time, beating well after each addition. Mix in the mashed bananas and vanilla extract until combined.
Gradually add the dry ingredients to the wet mixture, stirring with a spatula or wooden spoon just until combined. Do not overmix.
In a small bowl, toss the chopped strawberries with 1 tablespoon of flour until evenly coated. Gently fold the floured strawberries into the batter.
Pour the batter into the prepared loaf pan and spread evenly. Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. If the top browns too quickly, tent loosely with foil after 30 minutes.
Let the bread cool in the pan for 10 minutes, then lift out using the parchment overhang and transfer to a wire rack to cool completely before slicing. Serve on a rectangular platter.