Prep the pan: Line the bottom of a springform pan with parchment. Lightly mist the sides with nonstick spray to help clean release.
Make the crust: Stir crumbs, melted light butter, sweetener, and espresso powder (if using) until they feel like damp sand.
Press firmly into the bottom of the pan. Freeze for 10 minutes while you make the filling.
Heat the oven: Set to 325°F (163°C). Place a rack in the middle.
For extra insurance against cracks, put a shallow pan of hot water on a lower rack to add humidity.
Beat the cream cheese: In a large bowl, beat cream cheese with sweetener on medium speed for 1–2 minutes until smooth, scraping down the bowl. Avoid whipping in too much air.
Add yogurt and flavor: Mix in Greek yogurt, vanilla, espresso mixture, cornstarch, and salt. Blend just until smooth.
Add eggs: Beat in eggs one at a time on low speed until combined.
Stop as soon as the batter is uniform to keep it creamy.
Assemble and add coffee soak: Pour half the batter over the chilled crust. Lightly brush or drizzle the crust with a little of the cooled coffee (and liqueur if using)—do not oversoak. Pour in the remaining batter and smooth the top.
Bake: Bake for 40–50 minutes, until the edges are set and the center jiggles slightly like gelatin.
If the top browns quickly, tent it loosely with foil.
Cool gently: Turn off the oven, crack the door, and let the cheesecake rest inside for 30 minutes. Move to a rack and cool to room temperature.
Chill: Cover and refrigerate at least 6 hours, preferably overnight, for the best texture and flavor.
Finish: Right before serving, dust the top evenly with unsweetened cocoa powder using a fine sieve. Add a dollop of light whipped topping or sweetened Greek yogurt if you like, and garnish with shaved chocolate.