For crust, combine crumbs and 2 tablespoons sugar. Stir in butter, toss gently. Press onto bottom and 1 inch up sides of a 9-inch springform pan. Bake in 375 degree F oven about 10 minutes or until edges begin to brown. Cool slightly on a wire rack.
Meanwhile, for filling, combine cream cheese, 1 cup sugar, cinnamon, and apple-pie spice. Beat until fluffy. Beat in applesauce and lemon juice. Beat in eggs until combined.
Pour filling into crust-lined pan. Bake on a shallow baking pan in a 375 degree F oven 40 to 45 minutes or until center is nearly set. Cool on a wire rack 15 minutes. Loosen sides of pan. Cool 30 minutes more; remove sides. Cool completely. Chill at least 4 or up to 24 hours.
For sauce, in a small heavy saucepan melt 1/2 cup sugar over medium-high heat until sugar begins to melt, shaking pan often. (Do not stir.) Reduce heat; cook about 5 miutes more or until sugar is melted and golden. Stir as necessary after sugar begins to melt (only when mixture bubbles). Remove from heat. Carefully pour in 1/2 cup whipping cream. Add 1 tablespoon butter. Return to heat; cook and stir for 1 to 2 minutes more or until smooth. Stir in 1/3 cup coarsely chopped pecans. Cool. Cover and chill up to 24 hours. To serve, cut cheesecake into wedges; top with sauce. Makes 12 to 16 servings.