Prep the pan. Heat the oven to 325°F (165°C). Line the bottom of a 9-inch springform pan with parchment. Lightly mist the sides with nonstick spray.
Make the crust. Stir crushed graham crackers, melted butter, sugar or sweetener, and a pinch of salt until the texture resembles wet sand.
Press firmly into the bottom of the pan. Bake for 8–10 minutes until fragrant. Cool while you make the filling.
Cook the raspberry swirl. In a small saucepan, combine raspberries, sugar or sweetener, and lemon juice.
Simmer over medium heat for 5–7 minutes, stirring and mashing, until saucy. Strain through a fine sieve to remove seeds if you like. Cool to room temperature.
Beat the cream cheese. In a large bowl, beat softened cream cheese with sugar or sweetener and salt on medium speed until smooth and fluffy, about 2 minutes.
Avoid overbeating to limit air bubbles.
Add yogurt and flavorings. Mix in Greek yogurt, lemon zest, lemon juice, vanilla, and cornstarch until just combined and silky.
Add eggs. Beat in eggs and egg white one at a time on low speed, scraping the bowl as needed. Stop mixing as soon as the batter looks even and glossy.
Assemble. Pour the filling over the cooled crust. Dollop 8–10 spoonfuls of raspberry sauce on top.
Use a skewer or knife to gently swirl, keeping the pattern on the surface.
Bake gently. Place the springform on a rimmed baking sheet. Bake at 325°F for 40–50 minutes. The edges should be set, and the center should have a slight jiggle like Jell-O.
Do not overbake.
Cool slowly. Turn off the oven, crack the door, and let the cheesecake sit inside for 30 minutes. Then set it on a rack to cool completely.
Chill and serve. Cover and refrigerate at least 6 hours, preferably overnight. Release the springform, slice with a warm, clean knife, and garnish if you like.