Stir together graham cracker crumbs, melted butter, and sugar until the mixture looks like wet sand and holds together when squeezed. Press firmly into the bottom of a 9-inch springform pan using the bottom of a measuring cup to create an even layer. Chill while you make the filling.

In a large bowl, beat the room temperature cream cheese with an electric mixer on medium speed until completely smooth and fluffy, about 2 minutes. Scrape down the bowl twice to eliminate any lumps.

Add powdered sugar, lemon zest, and vanilla extract. Beat on medium-low until just combined, about 1 minute. Pour in the fresh lemon juice and beat briefly until incorporated.

In a separate clean bowl, whip the cold heavy cream on medium-high speed until stiff peaks form, about 3-4 minutes. The cream should hold its shape when you lift the beaters.

Gently fold about one-third of the whipped cream into the cream cheese mixture to lighten it, then fold in the remaining cream in two additions. Use a rubber spatula and a light hand - stop when no white streaks remain.

Pour the filling over the chilled crust and smooth the top with an offset spatula. Refrigerate uncovered for at least 4 hours, preferably overnight, until completely set and firm to the touch.

Run a thin knife around the edge of the pan before releasing the springform. Slice with a clean, warm knife for neat cuts. Serve chilled with extra whipped cream and lemon slices if desired.