In a large mixing bowl, beat the softened cream cheese until smooth. Add the powdered sugar and continue mixing until well combined. Gradually pour in the heavy cream and mix until smooth. Add the eggs, one at a time, mixing on low speed after each addition until just incorporated.
Add the vanilla extract and cornstarch. Mix on low speed until well combined. Strain the cheesecake batter through a fine-mesh sieve to remove any lumps and achieve a smooth texture.
Divide the batter into two portions, setting aside one-third for the matcha layer and leaving the remaining two-thirds for the plain cheesecake layer. Add the matcha powder to the smaller portion and gently mix with a spatula until smooth and evenly combined.
Pour the matcha batter into a parchment-lined baking pan with a removable bottom. Bake in a preheated oven at 470°F (240°C) for about 5 minutes, or until a thin skin forms on the surface.
Remove the pan from the oven and gently pour the remaining plain cheesecake batter over the matcha layer. Return the pan to the oven and bake for another 20–25 minutes, keeping an eye on the top to prevent excessive browning.
Once the cheesecake is baked, remove it from the oven and let it cool completely before slicing.
Notes
Check for doneness. The cheesecake is ready when the top is deeply browned, the edges are set, and the center still has a slight jiggle when the pan is gently shaken. Avoid overbaking to keep the texture rich and creamy.
Use the right baking pan. Use a deep, removable-bottom baking pan lined with parchment paper. Make sure the parchment paper extends above the rim, as the cheesecake will rise quite high during baking.
Mix the matcha powder properly. Sift the matcha powder into the reserved cheesecake batter and gently fold until smooth. Alternatively, whisk the matcha powder with a small amount of cold water until no lumps remain, then mix it into the batter. Use just enough water to dissolve the matcha without thinning the cheesecake batter too much.
Don't worry if the cheesecake deflates. The cheesecake will look quite tall and puffed up when it first comes out of the oven. As it cools, it will naturally sink and become shorter. This is completely normal for a Basque cheesecake, so don't worry!
Cool before slicing. Let the cheesecake cool completely, then refrigerate it for at least 4 hours or overnight. This helps the creamy layers set and gives you beautiful, clean slices.