Prep the pan and oven. Heat your oven to 350°F (175°C).
Grease a 9x5-inch loaf pan and line it with a parchment sling so the loaf lifts out easily. This helps prevent sticking and keeps the edges neat.
Mix dry ingredients. In a large bowl, whisk the flour, sugar, baking powder, and salt. Whisking breaks up clumps and distributes the leavening, so you get an even rise.
Whisk wet ingredients. In a separate bowl or large measuring cup, combine eggs, melted butter, yogurt, milk, lemon zest, lemon juice, and vanilla.
Stir until smooth. The yogurt and butter will look slightly creamy—this is perfect.
Combine gently. Pour the wet mixture into the dry ingredients. Stir with a spatula until just combined.
A few small streaks of flour are okay. Do not overmix, or the loaf can turn tough.
Fill the pan. Scrape the batter into the prepared pan. Smooth the top with a spatula and tap the pan lightly on the counter to release any large air bubbles.
Bake. Bake for 50–60 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs. If the top is browning too fast, tent it loosely with foil for the last 10–15 minutes.
Cool before glazing. Let the loaf cool in the pan for 10 minutes, then lift it out using the parchment and set it on a rack.
Cool until just warm to the touch, about 45 minutes. Glazing too hot will make the glaze melt away.
Make the glaze. In a small bowl, whisk powdered sugar with 2 tablespoons lemon juice. Add more juice, a teaspoon at a time, until it’s thick but pourable.
You want it to ribbon slowly off a spoon.
Glaze and set. Spoon or drizzle the glaze over the warm loaf, letting it drip down the sides. Sprinkle a bit of zest on top if you like. Let the glaze set for 20–30 minutes before slicing.
Slice and enjoy. Use a serrated knife for clean slices.
Serve plain or with a swipe of butter. It’s great with coffee, tea, or fresh berries.