Heat the oven to 350°F (175°C). Grease a 9-inch springform pan, line the bottom with parchment, and wrap the outside of the pan with two layers of heavy-duty foil to waterproof it.
Make the crust: In a bowl, combine the finely crushed graham crackers, 3 tbsp granulated sugar, fine salt, and melted unsalted butter until the crumbs are evenly moistened. Press firmly into the bottom and 1.5 inches up the sides of the pan. Bake until fragrant and just starting to color, 10–12 minutes. Cool on a rack 10 minutes, then reduce the oven to 325°F (165°C).
Set up the water bath: Place the foil-wrapped pan in a deep roasting pan. Bring a kettle of hot water or use very hot tap water so it’s ready to pour once the cake is filled.
Make the filling: In a mixer on medium-low, beat the softened cream cheese with 1 cup granulated sugar until completely smooth, 2–3 minutes, scraping the bowl. Mix in the 1.5 tbsp cornstarch, lemon zest, 1 tbsp lemon juice, and vanilla extract just to combine. Add the eggs one at a time on low speed, mixing only until incorporated, then blend in the sour cream until no streaks remain; do not overmix.
Pour the filling into the crust and smooth the top. Tap the pan gently on the counter a few times to release large air bubbles.
Slide the roasting pan onto the middle rack of the oven, then carefully pour hot water into the roasting pan to come halfway up the sides of the springform. Bake until the edges are set and the center wobbles like gelatin (a 2-inch circle in the middle should jiggle), 60–75 minutes.
Turn off the oven, crack the door, and let the cheesecake rest in the oven for 60 minutes. Remove from the water bath, unwrap the foil, run a thin knife around the edge, and cool on a rack to room temperature, about 1 hour. Cover and refrigerate until fully set, at least 6 hours or overnight.
Make the cherry topping: In a medium saucepan, combine the tart cherries, 0.5 cup water, and 0.75 cup granulated sugar. Bring to a simmer over medium heat and cook until the cherries soften and release juices, 3–5 minutes. Stir the 2 tbsp cornstarch together with 2 tbsp of the hot cherry liquid to make a smooth slurry, then stir it back into the pan and simmer until thick, glossy, and the sauce slowly mounds on a spoon, 1–2 minutes. Off heat, stir in 1 tbsp lemon juice and cool completely.
Unmold and finish: Remove the springform ring and transfer the cake to a platter. Spoon the cooled cherry topping over the chilled cheesecake and let stand 10 minutes so the topping sets. Slice with a hot knife, wiping between cuts, and serve.