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In a clean processor bowl, pulse cream cheese with sugar until very smooth. Add applesuace, yogourt, lemon juice and cinnamon; pulse until very well combined. Stir in eggs, just until uniformly combined.
Pour filling into prepared crust. Bake for 45 minutes. Turn off oven; let cheesecake stand in hot oven for 30 minutes. Remove to a rack; run a thin knife around edge of ring. Cool to room temperature, then chill for at least 2 hours.
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Stir sugar with pecans and flour in a small saucepan until well combined. Microwave cider in a heat-proof measure on high until steaming. Whisk into sugar mixture. Set over medium heat and cook, stirring constantly, until smooth and thickened. Whisk in butter. Serve cheesecake with warm sauce. Makes 12 to 16 servings.
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