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Coat bottom and sides of pan with nonstick spray. Line bottom with a parchment-paper round. Using your fingertips, mix crust ingredients in a medium bowl until mixture holds together when pinched. Pack onto bottom of pan in an even layer. Chill until firm, at least 1 hour.
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Place gelatin and 1 1/2 tablespoon cold water in a heatproof bowl. Let stand until softened, 5-10 minutes.
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Pulse cream cheese, yogurt, sugar, lemon juice, vanilla, and salt in a food processor, scraping down sides as needed, until completely smooth.
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Pour water to a depth of 1/2-inch into a small skillet over medium heat. Place bowl with gelatin in skillet; stir until gelatin dissolves, about 2 minutes. Remove bowl from skillet. With processor running, drizzle gelatin into cream cheese mixture; mix until well blended.
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Pour into prepared crust. Tap pan firmly on the counter to break up any big air bubbles. Smooth top. Cover tightly with plastic wrap and chill for at least 6 hours before serving.
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In a small bowl, stir together apples, 1/2 tsp cinnamon, nutmeg and lemon juice. Add 1 tablespoon butter to a skillet and melt over medium heat. Add apples and sugar and stir to coat. Sauté until apples begin to caramelize, about 6 minutes. Set aside to cool.
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Preheat oven to 350 degrees. Mix brown sugar, flour, oats and remaining 2 tablespoons butter in a bowl with fingers until coarse lumps form. Transfer to a baking sheet and spread in an even layer. Bake until golden brown, about 10 minutes. Allow to cool, then crumble mixture.
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To serve, gently remove cheesecake from springform pan and top with apples, streusel and caramel sauce.