Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan with butter or cooking spray, line the bottom with parchment paper, and grease the parchment.

In a medium bowl, whisk together the all-purpose flour, baking powder, and salt for about 30 seconds until combined and aerated.

Zest two lemons on a microplane to yield 2 tablespoons of zest. Juice the lemons, strain out any seeds or pulp, and reserve 5 tablespoons of juice.

In a large mixing bowl, beat the softened unsalted butter and granulated sugar on medium speed for 3 to 4 minutes until light, fluffy, and pale.

Add the three eggs one at a time, beating for about 1 minute after each addition until fully incorporated.

Stir the lemon zest, 3 tablespoons of lemon juice, and vanilla extract into the Greek yogurt. Add one-third of the flour mixture to the butter-egg mixture and fold gently with a spatula for about 10 to 15 strokes. Fold in half of the yogurt mixture, then another third of the flour, the remaining yogurt mixture, and finally the last of the flour, stopping when no flour streaks remain.

Pour the batter into the prepared pan and smooth the top with a spatula. Bake at 350°F (175°C) for 33 to 38 minutes, or until a wooden skewer inserted into the center comes out with just a few moist crumbs and the top is golden brown.

Let the cake cool in the pan for 10 minutes, then invert onto a wire rack and cool completely to room temperature, about 1 hour.

In a small bowl, whisk together the powdered sugar, 2 tablespoons of lemon juice, and lemon zest until smooth, adding up to 1 tablespoon of water if the glaze is too thick. Drizzle evenly over the cooled cake, let it set for at least 20 minutes before slicing.