Preheat the oven to 350°. Grease a 2-by-10-inch springform pan. Using a food processor, finely grind the cookies and almonds. Drizzle the melted butter over the crumbs; pulse briefly to mix. Transfer the mixture to the prepared pan and press evenly into the bottom. Bake the crust until golden, about 12 minutes. Wipe out the food processor.
In the food processor, combine the ricotta, egg yolks, 1/2 cup granulated sugar, lemon zest, vanilla and salt; pulse to blend. Add the flour and pulse until just incorporated. Do not overblend.
Using an electric mixer with the whisk attachment, beat the egg whites on medium speed until foamy. Continue to beat, gradually sprinkling in 1/2 cup granulated sugar, until glossy and stiff but not dry. Add one-third of the ricotta mixture to the egg whites and fold in gently with a rubber spatula until half-blended. Repeat with the remaining ricotta mixture in 2 more batches.
Pour the batter into the prepared crust and bake until the top is brown and puffed, about 1 hour 15 minutes. (If the cake is well browned after 1 hour but still jiggly when the pan is touched, turn off the oven and leave the cake in with the door closed for 15 minutes more.). Transfer the pan to a rack and let cool completely.
In a small saucepan, simmer the cranberries, the remaining 3/4 cup sugar and 1/2 cup water over medium heat until the berries burst, about 5 minutes. Transfer the cranberry compote to a bowl and let cool completely.
Dust the top of the cheesecake with the confectioners sugar, if using. Serve with the compote.