Heat oven to 350°F. Grease 9-inch springform pan with 1 tablespoon butter. In medium bowl, mix 1 1/4 cups pecans, the bread crumbs and 2 tablespoons granulated sugar. Drizzle melted butter over pecan mixture; toss to combine. Press into bottom and up side of pan; refrigerate.
In large bowl, beat cream cheese until fluffy. Gradually beat in 1 cup brown sugar and 2/3 cup granulated sugar until smooth. Beat in 5 eggs, 1 at a time, until well blended. In small bowl, mix flour, pumpkin pie spice, pumpkin and brandy. Gradually add to cream cheese mixture; beat until smooth. Pour into crust.
Bake 1 hour 20 minutes to 1 hour 30 minutes or until center is set. Turn oven off; let cheesecake stand in oven with door open at least 8 inches for 30 minutes. Remove from oven; cool to room temperature on cooling rack. Remove side of pan. Refrigerate overnight.
In small saucepan, heat 1/2 cup brown sugar, the water and 1/4 cup butter to boiling over medium heat; boil 2 minutes. Gradually blend small amount of hot syrup into beaten egg. Return egg mixture to saucepan; cook over low heat 1 minute, stirring constantly. Remove from heat; stir in 1/4 cup pecans and the vanilla. Serve sauce slightly warm over each wedge of cheesecake.