Prep your pan and oven. Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line it with a parchment sling, leaving overhang for easy removal.
Lightly flour the pan, tapping out the excess.
Mix the dry ingredients. In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
Beat the butter and sugar. In a large bowl, use a hand mixer or stand mixer to beat softened butter and granulated sugar on medium-high until pale and fluffy, about 3 minutes. This step traps air and helps the cake rise.
Add the eggs. Beat in the eggs one at a time, mixing well after each addition.
Scrape down the bowl as needed so everything is fully combined.
Flavor boost. Finely zest both lemons directly into the bowl to catch the oils, then add the vanilla. Mix just until blended. Juice the lemons and set aside for the glaze and batter.
Combine wet ingredients. In a small bowl or measuring cup, whisk together sour cream, milk, and 2 tablespoons of fresh lemon juice.
Bring it all together. Add the dry ingredients to the butter mixture in three additions, alternating with the sour cream mixture (dry-wet-dry-wet-dry).
Mix on low just until smooth. Avoid overmixing to keep the crumb tender.
Fill the pan. Spoon the batter into the prepared loaf pan and smooth the top. Tap the pan gently on the counter to release any large air bubbles.
Bake. Bake for 55–70 minutes, until the top is golden and a toothpick inserted in the center comes out mostly clean with a few moist crumbs.
If the top browns too quickly, tent loosely with foil during the last 15 minutes.
Cool. Let the cake cool in the pan for 15 minutes. Lift it out using the parchment and transfer to a wire rack to cool completely before glazing.
Make the glaze. Whisk powdered sugar with 3 tablespoons lemon juice until smooth and pourable. Add an extra tablespoon of juice if needed to thin.
Stir in lemon zest if you like it extra bright.
Glaze and set. Pour the glaze over the cooled cake, letting it drip down the sides. Allow 20–30 minutes for the glaze to set before slicing.