Preheat the oven to 350°F (175°C). Line a 9-inch square baking pan with parchment paper to prevent sticking.
In a mixing bowl, whisk together the all-purpose flour, baking powder, salt, and sifted matcha powder until well combined and evenly distributed.
In a separate large bowl, beat the eggs with granulated sugar using a whisk until the mixture becomes frothy and light in color, about 2-3 minutes. Add the vegetable oil and vanilla extract, and whisk until smooth.
Gradually add the dry ingredients to the wet mixture, folding gently with a spatula until just combined and there are no dry streaks. The batter will be thick but pourable.
Gently fold in the sliced strawberries, distributing them evenly throughout the batter.
Pour the batter into the prepared baking pan and smooth the top with a spatula. Bake in the preheated oven for 20-25 minutes, or until the cake is golden and a toothpick inserted into the center comes out clean. Allow to cool slightly before slicing.