Heat oven to 325°F; set a rimmed pan of hot water on lower rack.
Grease a 9-inch springform; line the bottom with parchment.
Stir crumbs, brown sugar, and salt in a bowl.
Pour in melted butter; mix until evenly moistened.
Press crumbs into pan base and slightly up sides.
Bake crust 8 minutes; cool on a rack.
Simmer cranberries, sugar, juice, and water in a saucepan.
Cook until berries burst and mixture thickens, 8–10 minutes.
Stir in orange zest; cool until barely warm.
Beat cream cheese and sugar until fluffy, about two minutes.
Mix in sour cream, vanilla, lemon zest, and cornstarch.
Beat in eggs one at a time on low.
Spread half the batter over crust; dot with cranberry sauce.
Swirl gently with a knife; add remaining batter and more sauce.
Swirl again lightly; tap pan to release bubbles.
Bake until edges set and center wobbles, 55–65 minutes.
Cool one hour on a rack; chill at least four hours.
Slice with a warm knife; serve with extra sauce.
Notes
No cranberries? Use a quick raspberry sauce. Swap gingersnaps for the crust if you like more spice. No sour cream handy? Greek yogurt works. If skipping the water pan, drop oven to 300°F and add 10–15 minutes.