Prep the pan. Preheat oven to 180°C (350°F). Then grease and line a loaf pan (8x4 or 9x5 inch).
Rub the zest into the sugar. In a large bowl, rub the lemon zest into the sugar with your fingers for about a minute until it looks damp and smells fragrant.
Whisk in the wet ingredients. Add the melted butter, eggs, vanilla, lemon juice, yogurt, and milk. Whisk until smooth.
Add the dry ingredients. Add the flour, baking powder, and salt directly into the bowl. Mix gently just until combined, the batter should look thick and smooth with no dry streaks.
Bake. Pour batter into the prepared pan and bake 38 to 40 minutes for an 8x4 pan, or 30to 35 minutes for a 9x5 pan, or until a toothpick comes out clean. (I used an 8x4 pan for this recipe for a taller loaf cake).
Make the syrup. While the loaf bakes, combine the syrup ingredients in a bowl and microwave 40-60 seconds, or heat gently in a small pot until the sugar dissolves.
Soak it while it's hot. Pour the warm syrup over the loaf immediately after it comes out of the oven. Let it soak in as the loaf cools in the pan, this is what keeps it so moist.
Glaze. Whisk the glaze ingredients together and drizzle over the top.
Slice and enjoy!