Preheat oven to 325°F. Line the bottom of a 9-inch springform pan with parchment and lightly grease the sides. Wrap the outside of the pan with 2 layers of heavy-duty foil for a water bath.
Make the crust: Stir graham crumbs, 0.25 cup sugar, and melted butter until evenly moistened. Press firmly into the bottom of the pan. Bake 10 minutes, then cool while you prepare the filling.
Whisk matcha with hot water to form a smooth lump-free paste; let cool 2 minutes.
Beat cream cheese and 0.75 cup sugar on medium-low until smooth and creamy, about 2 minutes. Scrape bowl.
Mix in sour cream, heavy cream, vanilla, lemon juice, cornstarch, and salt on low until combined.
Beat in eggs one at a time on low speed just until incorporated, scraping the bowl after each addition. Do not overmix.
Blend in the matcha paste until the batter is evenly green.
Pour batter over the crust. Tap the pan gently to release air bubbles. Place the pan in a deep roasting pan and pour hot water around it to reach halfway up the sides.
Bake 55 to 65 minutes, until edges are set and the center wobbles like gelatin. Turn off oven, crack the door, and let the cheesecake cool inside for 1 hour.
Remove from water bath, unwrap foil, run a thin knife around the edge, and cool to room temperature. Chill covered for at least 4 hours or overnight before slicing.
Release the springform, transfer to a platter, and slice with a warm clean knife. Serve as is or with lightly sweetened whipped cream.
Notes
For best color and flavor, use fresh, high-quality matcha and avoid overbaking. A gentle jiggle in the center ensures a creamy texture.