1. Preheat the oven to 350F.

2. Melt the stick of butter in a small saucepan over low heat.

3. Meanwhile, butter a 10-inch springform pan liberally, making sure to get butter into the edges of the pan.

4. Place the pan on a large square of aluminum foil, and fold the corners of the foil up around the outsides of the pan. (This just makes clean-up easier if any butter oozes out the bottom of the pan during baking.) Place the foil-bottomed springform pan on a baking sheet, and set aside.

5. Make the gingersnap crumbs by whirling gingersnaps in a food processor until finely chopped, or place the cookies in a zip-top plastic bag and roll with a rolling pin until well-crushed. When the butter has melted, add the gingersnap crumbs and the confectioners’ sugar to the butter, and stir to blend.

6. Dump the crust mixture into the springform pan, and use the palms of your hands to press the crust into an even layer on the bottom of the pan. Transfer the pan to the freezer to chill while you make the batter.

7. In a stand mixer fitted with the paddle attachment (or using an electric mixer), whip the cheeses together for 3 minutes on medium speed, until smooth and light. Use a rubber scraper to loosen any unwhipped cheese from the paddle and bottom of the bowl.

8. Whip again on medium speed for another minute or two, adding the granulated sugar in a slow, steady stream.

9. Add the eggs, one at a time, scraping down the sides of the bowl between additions, then add the vanilla.

10. Mix the batter on medium-high speed for 2 minutes more, scraping the sides and bottom of the bowl, and the paddle, halfway through.

11. Return the springform pan to the baking sheet and pour the batter into the pan.

12. Bake for 60 to 65 minutes, or until the cake moves as a whole when you tap the sides of the pan and appears set in the center. (It may crack; that’s okay.)

13. Cool at least 30 minutes.

14. While the cake bakes, combine the vinegar and the honey in a small saucepan and bring to a strong simmer. Simmer for about 15 minutes, or until the mixture begins to look syrupy.

15. Transfer to a bowl and refrigerate until cool. (The mixture should thicken considerably in the refrigerator.)

Note: You can make the cake up to this point 2 days before serving. Cover the cake loosely with plastic wrap and refrigerate until ready to serve.

Just before serving, halve and pit the cherries, and fold them into the balsamic mixture. Serve the cake topped with the cherries.