• Preheat oven to 350°F. Line a 9x13-inch baking dish with parchment paper, leaving some overhang for easy removal.
• In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
• In a large bowl using a handheld mixer or stand mixer fitted with the paddle attachment, beat the butter and granulated sugar on high speed until smooth and creamy, about 3 minutes. Scrape down the sides and bottom of the bowl as needed.
• Add the eggs and vanilla extract; beat on high speed until fully combined, about 2 minutes. Scrape down the bowl again.
• With the mixer on low speed, add the dry ingredients in three additions, mixing just until combined after each. Do not overmix.
• Slowly pour in the milk, then add the lemon zest and lemon juice. Mix just until everything is incorporated and no large lumps remain. The batter will be slightly thick.
• Pour the batter into the prepared baking dish and spread it into an even layer.
• Bake for 28 to 35 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs, but no wet batter. (Start checking at 28 minutes; if the edges brown too quickly, loosely tent with foil.)
• Remove from the oven and place the pan on a wire rack. Let the cake cool completely in the pan before glazing.

Lemon Glaze

• In a medium bowl, whisk together the confectioners' sugar, lemon juice, and milk until smooth and glossy. Add more lemon juice, a teaspoon at a time, for a thinner glaze, or more confectioners' sugar for a thicker glaze.
• Pour the glaze over the top and gently spread it to the edges of the cake.
• Allow the glaze to set at room temperature for 20 to 30 minutes before cutting and serving.