1. Place a rack in middle of oven; preheat to 350°. Coat a 9-inch springform pan with cooking spray; set aside.
2. To make cake crust: Place almonds, flour, and sugar in a food processor; process until nuts are finely ground. Add butter; pulse until combined. Press crust evenly over bottom of prepared pan. Bake until golden brown (about 15 minutes). Transfer to a wire rack; cool completely. Reduce oven heat to 300°.
3. Place cream cheese in a large bowl; beat with an electric mixer at medium-high speed until light and fluffy (about 2 minutes). Gradually add condensed milk, amaretto, and vanilla to mixture; beat until smooth, scraping down sides of bowl as necessary. Reduce mixer speed to medium; add eggs, one at a time, beating well after each addition. Pour batter into prepared pan. Bake until cheesecake is puffed on sides and slightly jiggly in center (55-60 minutes). Let cool completely on a wire rack. Tightly cover and refrigerate until thoroughly chilled and set (at least 8 hours or up to 2 days).
4. To make brittle: Increase oven heat to 350°. Place almonds on a baking sheet; toast until golden brown and fragrant (about 5-7 minutes), stirring twice. When cool, push almonds close together in an 8-inch circle. Heat a medium heavy saucepan over medium heat; add sugar, water, and salt to pan, stirring until sugar dissolves. Increase heat to high; bring mixture to a boil, washing down sides of the pan with a wet pastry brush to remove sugar crystals. Boil, without stirring, until caramel is a dark amber color, then swirl the pan to even out the color. Immediately pour caramel in a circular motion evenly over almonds on baking sheet, coating well. Allow brittle to cool and harden (about 15 minutes). Break into smaller pieces; place in a large zip-top plastic bag. Crush brittle into 1/2-inch pieces with a rolling pin.
5. To serve, run a knife around inside edge of pan to loosen cake; remove side of pan. Using your palms, coat side of cheesecake with praline pieces; carefully press remaining praline pieces into top of cake. Cut cheesecake into wedges with a serrated knife dipped into hot water; wipe knife dry after each cut.