Prep your pan and oven: Heat the oven to 350°F (175°C). Line a 9x5-inch loaf pan with parchment, leaving overhang for easy removal. Lightly grease the parchment and sides.
Zest and juice the lemons: Zest 2 large lemons, avoiding the bitter white pith. You should have about 1–1.5 tablespoons of zest. Juice the lemons and set aside 1/3 cup of juice total (some for the batter, some for the glaze).
Mix the dry ingredients: In a medium bowl, whisk 1.5 cups all-purpose flour, 1.5 teaspoons baking powder, and 1/2 teaspoon fine salt. Set aside.
Cream the butter and sugar: In a large bowl, beat 1/2 cup unsalted butter with 3/4 cup granulated sugar until light and fluffy, 2–3 minutes. This step builds structure and helps the cake rise.
Add eggs and flavorings: Beat in 2 large eggs, one at a time, until fully combined. Mix in 1 teaspoon vanilla extract and the lemon zest. Scrape the bowl as needed.
Add yogurt and lemon juice: Stir in 1/2 cup plain yogurt and 2 tablespoons fresh lemon juice until smooth. The mixture may look slightly curdled; that’s fine.
Combine wet and dry: Add the dry ingredients to the bowl and mix gently just until no dry streaks remain. If you like an extra-moist loaf, fold in 2 tablespoons neutral oil at the end. Do not overmix.
Fill the pan: Spread the batter into the prepared pan and smooth the top. Tap the pan lightly on the counter to release air bubbles.
Bake: Bake for 45–55 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs. If the top browns too quickly, tent it with foil for the last 10 minutes.
Cool and glaze: Let the loaf cool in the pan for 10 minutes. Lift out using the parchment and transfer to a wire rack. While warm, whisk 1 cup powdered sugar with 2–3 tablespoons lemon juice until smooth and pourable. Brush or spoon half the glaze over the warm loaf so it soaks in, then let it cool completely. Once cool, drizzle the remaining glaze on top for a glossy finish.
Slice and serve: Use a sharp serrated knife for neat slices. Wipe the blade between cuts for clean edges.