Preheat oven to 325°F. Grease and line two 8-inch pans with parchment paper. Set aside.
In a medium-size bowl, beat together butter and sugar until light and fluffy, about 5 minutes. Add in the eggs, one at a time, beating well after each addition.
Add the sifted matcha powder and vanilla, beat until combined. Combine the flour, baking soda, and salt in a bowl.
Add half of the flour mixture to the batter and beat on low speed. Add the milk and yogurt, and beat again. Add the remaining flour mixture and fold it in with a spatula until no streaks of flour remain. Be careful not to overmix the batter.
Pour the batter into the prepared pan, and bake for about 30-35 minutes or until a toothpick inserted comes out clean.
Remove from pan and place on a rack to cool completely.
For the frosting: in a separate bowl, beat the heavy cream and sugar together until light and fluffy. Set aside.
Level your cakes with a serrated knife and spread some whipped cream on top of one cake. Top with the second layer of cake and cover the top with the remaining frosting.
Decorate with strawberries and enjoy!
Notes
* Don't have cake flour? Combine 1¾ cups all-purpose flour and ¼ cup cornstarch, sift at least 3 times.