In 2-quart saucepan, heat sugar and water to boiling, stirring constantly, until sugar is dissolved. Reduce heat to medium-high; boil, without stirring, 7 to 8 minutes or until syrup is golden, swirling pan occasionally. (Wash down sides of pan with water, using a pastry brush, if sugar crystals form on sides.) Remove from heat; gradually stir in warm cream and bourbon (mixture will bubble up). Cool completely.
Heat oven to 375°F. Spray 9-inch tart pan with removable bottom with cooking spray. Place pie crust in pan as directed on box for One-Crust Filled Pie. Press in bottom and up sides of pan; trim edges if necessary. Add butter and egg to sugar syrup, stirring until smooth. Stir in peanuts and chocolate chips. Pour filling into crust-lined pan. Bake 36 to 38 minutes. Cool completely on cooling rack. Serve with whipped cream.