Preheat your oven to 350°F (175°C). Grease an 8-inch cake pan and line the bottom with parchment paper.
In a large mixing bowl, whisk together the sifted flour, matcha powder, and half of the sugar until evenly combined. The dry mixture should look vibrant green and slightly powdery.
In a separate bowl, whisk the eggs with the remaining sugar until the mixture turns pale and slightly thickened, about 2-3 minutes. You should see a light, airy quality and a sweet aroma.
Pour in the melted butter gradually while whisking gently to incorporate it smoothly into the egg mixture. This helps create a cohesive, rich batter.
Alternate adding the dry ingredients and milk to the wet mixture, starting and ending with the dry. Fold gently with a spatula each time until just combined, being careful not to deflate the batter.
Pour the batter into the prepared cake pan, smoothing the top with a spatula. Tap gently on the counter to release any large air bubbles.
Bake in the preheated oven for about 35 minutes or until the cake springs back lightly when pressed and a toothpick inserted in the center comes out clean.
Remove the cake from oven and let it cool in the pan for 10 minutes before transferring to a wire rack to cool completely. This prevents it from cracking.
Once cooled, carefully split the cake horizontally into two layers if desired. Spread the strawberry puree over the bottom layer, then place the top layer back on to form a sandwich.
Mix the powdered sugar with a teaspoon of water to create a slightly thick glaze. Drizzle it over the top of the cake for a glossy finish and a touch of sweetness.
Slice and serve this delicate cake with a dusting of extra powdered sugar or fresh strawberry slices for garnish. Enjoy the tender texture and vibrant flavor pairing.