Preheat the oven. Preheat oven to 400°F (204ºC). Line a 12-cup standard muffin tin with paper liners.
Make the lemon sugar. In a large mixing bowl, combine the sugar (1 1/4 cups) and lemon zest (3 tablespoons). Rub them together with your fingertips for 30–60 seconds, until the sugar feels slightly damp and smells very fragrant. This helps release the lemon oils and gives the muffins a brighter, more pronounced lemon flavor.
Mix the dry ingredients. In a medium bowl, whisk together the flour (2 1/2 cups), cornstarch (1 tablespoon), salt (1/4 teaspoon), baking powder (2 1/2 teaspoons), baking soda (1/2 teaspoon), and poppy seeds (2 tablespoons) until well combined.
Mix the wet ingredients. To the bowl with the lemon sugar, whisk in the egg (1) and egg yolk (1) until smooth. Add the sour cream (2 tablespoons), buttermilk (1 cup), vegetable oil (1/2 cup), lemon juice (1/4 cup), and vanilla (2 teaspoons), then whisk until the mixture is smooth and fully combined.
Combine the batter. Pour the wet ingredients into the dry ingredients and stir gently just until combined. Do not overmix. The batter should still look a little lumpy.
Let the batter rest. Let the batter sit for 10 minutes before baking. This gives the flour time to fully hydrate and helps create a softer, more tender muffin.
Fill the muffin tin. Divide the batter evenly among the muffin cups, filling each one about ¾ to nearly full, about a heaping ⅓ cup batter per muffin. This helps create tall, bakery-style muffin tops.Let the filled muffin pan rest for 5 minutes before baking. This allows the leavening to begin activating and helps produce taller, bakery-style muffin tops. Bake the muffins. Bake at 400°F for 5 minutes. Then, without opening the oven door, reduce the oven temperature to 350°F and continue baking for 13–16 minutes, or until the tops are lightly golden and a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Cool the muffins. Let the muffins cool in the pan for 10 minutes, then transfer them to a wire rack to cool further.
Make the glaze. In a small bowl, whisk together the powdered sugar (1 cup) and 2 tablespoons lemon juice. Add a little more lemon juice, if needed, until the glaze is thick but pourable.
Glaze and serve. Drizzle the glaze over the muffins once they’ve cooled slightly. Let the glaze set, then serve.