1. Preheat the oven to 400°F. Lightly grease a 10-inch springform pan.
2. For the crust: In a mixing bowl with a paddle, combine the flour, sugar, salt, and butter. Mix until the mixture is crumbly, then add the egg and continue to mix until a soft dough forms.
3. Press the dough on the bottom and an inch up the sides of the prepared pan; dock with a fork, and bake for 15 minutes, until light golden brown. Remove from the oven and cool to room temperature. Reduce the oven temperature to 325°F.
4. For the filling: Place the cream cheese in a large mixing bowl with a paddle. Add the sugar and flour, and mix at low speed until there are no lumps. Scrape the bottom and sides of the bowl at least twice during this process, to be sure no cheese is sticking.
5. Add the lemon zest, salt, and vanilla, and mix to combine. Add the eggs, one at a time, mixing until incorporated and scraping the mixing bowl between additions. Stir in the sour cream.
6. Pour the filling over the crust and bake for 45 to 50 minutes, until the edges of the cake are set one inch in from the edge. The middle should still jiggle when you nudge the pan; in fact, the cake will look underbaked. Measure the temperature of the cake an inch from the edge: when it reaches 175°F, turn off the oven.
7. Prop open the door, and let the cheesecake cool slowly in the oven for 1 hour. During this time the center will finish setting. Cooling the cake slowly will keep the top from cracking and ensure a smooth, even texture inside.
8. For the glaze: Whisk together the water, sugar, and cornstarch in a medium saucepan until the cornstarch dissolves. Place over medium heat and cook, stirring constantly, until the mixture boils, becomes clear, and thickens.
9. Remove from the heat and add the food coloring and the drained cherries. Let the mixture cool to room temperature, then spoon it over the cooled cheesecake. Refrigerate the cake until you're ready to serve.