Preparation

Make the compote

• Combine the cherries, sugar, Kirsch, cornstarch, and salt in a medium saucepan. Cook, simmering, over medium-high heat, stirring occasionally, until the cherries break down and the sauce around them thickens, 15 to 20 minutes for fresh cherries and about 30 minutes for frozen.
• Off the heat, stir in the almond extract. Transfer the compote to a bowl, and allow to cool to room temperature. Cover and refrigerate until cold. The compote will keep up to a week in the refrigerator, tightly covered.

Make the crust

• Apply a light film of cooking spray or butter to a 9-inch springform pan. Line the bottom and side with parchment paper. (To line the side of the pan, cut a strip of parchment a little longer than the circumference of the pan and a little taller than the pan. Press the parchment against the side of the pan.) Set aside.
• Put the cracker crumbs, sugar, and salt in the bowl of a food processor, and process until finely ground. Add the toasted nuts, and pulse to chop finely, about 8 pulses. Add the melted butter, and process, scraping down the bowl with a silicone spatula if necessary, until the crumbs are uniformly moistened.
• Transfer the crumbs to the prepared pan and firmly press them into the bottom and about two-thirds of the way up the side of the pan. (I find it easier to start with the side.) After pressing with your fingers, use a measuring cup or straight-sided glass to tightly secure the crumbs into place. Freeze the crust for at least 1 hour and up to overnight.

Make the filling and assemble the cake

• Put the cream cheese in the bowl of a stand mixer fitted with the paddle attachment, and beat on medium-low speed until smooth, about 2 minutes, scraping the bowl with a silicone spatula as needed. Slowly add the condensed milk and then the salt, scraping down the bowl as needed. Once smooth, add the lemon juice and extracts, beating until combined, about 1 minute.
• Transfer the filling to the prepared crust, smoothing the top with an offset spatula or butter knife. If you like, drizzle a few teaspoons of juice from the compote on top of the cake, and with a long toothpick or skewer, use the juice to make designs or swirls in the top of the cake. Cover the cake with plastic wrap, and refrigerate at least 5 hours, preferably overnight.

Serve the cake

• Release and remove the side of the pan. Carefully peel away and discard the parchment around the cake. To remove the bottom, slide a long, thin knife between the crust and the bottom to loosen, and then slide the cake onto a serving plate with a large spatula. Slice into wedges with a serrated knife, and serve each slice with some of the compote. Run the knife under hot water before making each cut to ensure clean slices.