Prep the pan and oven. Heat the oven to 350°F (175°C).
Line a 9x5-inch loaf pan with parchment, leaving an overhang for easy lifting. Lightly grease the sides.
Cream butter and sugar. In a large bowl, beat the softened butter and granulated sugar together until pale and fluffy, about 2–3 minutes. This helps create a light crumb.
Add eggs and zest. Beat in the eggs one at a time, mixing well after each.
Add the lemon zest and vanilla, then mix until just combined. If the batter looks slightly curdled, don’t worry—it will come together with the dry ingredients.
Combine dry ingredients. In a separate bowl, whisk together the flour, baking powder, and salt. This ensures even leavening.
Finish the batter. Add half the dry mixture to the wet ingredients and mix on low just to combine.
Add the milk or yogurt, then the remaining dry ingredients. Mix gently until no streaks of flour remain. Do not overmix.
Bake. Scrape the batter into the prepared pan, level the top, and bake for 45–55 minutes.
The cake is done when a skewer inserted in the center comes out clean or with a few moist crumbs.
Make the drizzle. While the cake bakes, stir together the lemon juice and sugar until the sugar begins to dissolve. You want a pourable mixture with a slight grain for a delicate crust.
Pierce and soak. Let the cake cool in the pan for 10 minutes. Poke holes all over the top with a skewer or toothpick.
Slowly spoon the lemon drizzle over the warm cake, letting it soak in. Use it all for full flavor.
Cool completely. Leave the cake in the pan until most of the drizzle has absorbed, then lift it out to a rack to cool completely.
Optional glaze. For a glossy top, whisk powdered sugar with just enough lemon juice to make a thick, pourable glaze. Drizzle over the cooled cake and let set for 20–30 minutes before slicing.