Whisk yogurt and sugar together until smooth, then whisk in eggs, oil, lemon zest, and vanilla until emulsified.

In a separate bowl, whisk the 1¾ cups flour, baking powder, and salt. Fold the dry mix into the wet just until combined. Toss blueberries with the 1 tbsp flour, then fold them in gently.

Preheat oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line with parchment. Scrape in the batter, smooth the top, and bake 50 to 55 minutes until golden and a toothpick comes out clean. Cool in pan 10 minutes, then transfer to a rack to cool completely.

Whisk powdered sugar with 1 tbsp lemon juice, adding more juice as needed to make a thick pourable glaze. Drizzle over the cooled cake, let set, and slice.