Preheat the oven to 350°F (175°C). Line the 9x13 inch baking pan with parchment paper, leaving an overhang for easy removal.
In a large mixing bowl, cream together the softened butter and granulated sugar until the mixture is pale and fluffy, about 2-3 minutes, and observe the color lightening and texture smoothening.
Add eggs one at a time to the creamed mixture, beating well after each addition, until the batter is smooth and slightly thickened. Smell the mixture for a hint of richness.
In a separate bowl, whisk together the flour, baking powder, and lemon zest. Gradually add the dry ingredients to the wet mixture, alternating with milk, beginning and ending with the dry ingredients, and mix until just combined. The batter should be smooth with no streaks.
Gently fold the pureed strawberries into the batter until evenly distributed, creating swirls of red throughout the pale yellow cake mixture.
Pour the batter into the prepared baking pan, spreading evenly with a spatula. Bake for 30-35 minutes until the top is golden brown, a toothpick inserted in the center comes out clean, and the edges start to pull away from the pan.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely. The cake should be moist with a tender crumb and visible strawberry swirls on the surface.
To make the glaze, whisk together powdered sugar, lemon juice, and a splash of water until smooth and glossy. Pour the glaze over the cooled cake, allowing it to drip down the sides. Garnish with fresh strawberry slices for color and texture.
