Preheat oven to 350°F. Grease a 9x5 inch loaf pan and line with parchment paper.
Mash bananas in a large bowl. Whisk in both sugars, melted butter, yogurt, eggs, and vanilla until smooth.
In a separate bowl, whisk flour, baking soda, baking powder, salt, and cinnamon.
Pour dry ingredients into wet. Fold gently until just combined. Do not overmix.
Toss diced strawberries with 1 teaspoon flour. Gently fold into batter along with any add-ins.
Spread batter into prepared pan. Sprinkle with coarse sugar if desired.
Bake 55 to 65 minutes, rotating halfway, until a toothpick comes out with moist crumbs.
Cool in pan 15 minutes, then transfer to a wire rack to cool completely.