Preparation Steps

• Arrange a rack in the center of the oven and preheat to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper leaving an overhang for easy removal and lightly butter the parchment.
• Grate the lemon zest into the sugar and rub them together with your fingertips until the sugar is fragrant and pale yellow — this infuses the sugar with citrus oil and intensifies the lemon flavor.
• In a large bowl, beat the softened butter and lemon-scented sugar on medium speed until fluffy, about 2–3 minutes. Add the oil in a slow stream while continuing to beat so the mixture stays emulsified.
• Crack the eggs into a small bowl and add them one at a time to the butter mixture, scraping the sides between each addition and beating until combined. Stir in the Greek yogurt and vanilla until smooth.
• Whisk together the flour, baking powder, baking soda, and salt in a separate bowl. Fold the dry ingredients into the wet mixture in two additions, folding just until there are no streaks of flour. Gently fold in the poppy seeds if using.
• Scrape the batter into the prepared pan and spread it evenly with an offset spatula. Tap the pan once on the counter to remove large air bubbles.
• Bake on the center rack for 30–34 minutes, or until the top is golden and a toothpick inserted into the center comes out with a few moist crumbs attached. Avoid overbaking to keep the cake tender.
• Allow the cake to cool in the pan on a wire rack for 20 minutes, then use the parchment overhang to lift it out and finish cooling to room temperature on the rack while you make the frosting.
• For the frosting: beat the softened butter by itself for 1–2 minutes until pale. Add the sifted powdered sugar and beat on low until combined, then increase speed and whip until light, about 1 minute.
• Add the cold cream cheese in small chunks and beat on medium until smooth and fully incorporated, 2–3 minutes. Mix in the vanilla, then drizzle in the lemon juice and beat just until glossy and spreadable. Chill the frosting 15–20 minutes if it seems too soft to pipe.
• Spread or pipe the frosting over the cooled sheet cake. For a simple ombré effect, divide the frosting into two bowls and tint one very lightly with a tiny pinch of turmeric (optional) or leave both natural and swirl with a spatula. Garnish with thin lemon slices or extra lemon zest.
• Slice and serve. Store any leftovers covered in the refrigerator for up to 3 days; allow slices to come to room temperature 20–30 minutes before serving for the best texture.