Preheat oven to 350°F (175°C). Grease a 9×5-inch loaf pan and line with a parchment sling for easy removal. Lightly flour the sides if desired.
In a large bowl whisk together flour, baking powder, baking soda, and salt until evenly combined.
In a separate bowl whisk the sugar, eggs, oil, yogurt, and vanilla until smooth and slightly thickened.
Pour the wet mixture into the dry ingredients. Stir gently with a spatula just until no large flour streaks remain. The batter will be thick.
Toss diced strawberries with the extra tablespoon of flour. Gently fold them into the batter so they are evenly distributed without overmixing.
Scrape the batter into the prepared pan and smooth the top. Bake 55–65 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs. The top should be golden and the center should spring back lightly when pressed.
Let the loaf cool in the pan for 15 minutes, then lift out onto a wire rack. Cool fully before glazing so the glaze does not melt and run off.
Whisk powdered sugar, 2 tablespoons milk, and vanilla until smooth. Add more milk a teaspoon at a time if needed for a thick but pourable consistency. Drizzle or spread over the cooled loaf. Let the glaze set 20–30 minutes before slicing.