1. Preheat the oven to 325°F. Grease an 8×8-inch baking pan and line it with parchment paper, leaving some overhang on the sides.

2. In a large bowl, beat the cream cheese with an electric mixer until smooth and creamy. Gradually add in the sugar and continue mixing until well combined.

3. Add the eggs one at a time, beating well after each addition. Mix in the flour and vanilla extract until just combined.

4. Divide the batter evenly into two separate bowls. To one bowl, fold in the strawberry purée until well incorporated. To the other bowl, stir in the matcha powder until combined.

5. Dollop the strawberry batter and matcha batter into the prepared pan, alternating between the two. Use a knife or a toothpick to swirl the batters together.

6. Bake for 45-50 minutes, or until the center is almost set. Allow the bars to cool completely in the pan before cutting and serving.