Grease an 8x4-inch loaf pan with nonstick spray and set aside.
In a large bowl, whisk together 2 cups flour, baking powder, baking soda, and salt until combined. Set aside.
In a medium bowl, whisk together the egg, granulated sugar, Greek yogurt, vegetable oil, and 1 teaspoon vanilla extract until smooth.
Add the wet ingredients into the bowl of dry ingredients and mix until just combined.
In a separate small bowl, combine the chopped strawberries with 1 tablespoon flour until coated.
Gently fold the strawberry mixture into the batter.
Pour batter into the prepared loaf pan.
Bake for 60-70 minutes, loosely covering the bread about halfway though, until the bread is golden brown and a toothpick inserted into the center comes out clean.
Remove bread from the oven and let cool completely.
In a small bowl, whisk together the confectioners' sugar, ½ teaspoon vanilla extract, and milk until you reach a drizzling consistency.