Line a 15x10x1-in. baking pan with foil; spray foil with cooking spray. Sprinkle with 2 cups peanuts; set aside.
In a small heavy saucepan, combine 3/4 cup sugar, 2/3 cup corn syrup and 1/4 cup water. Bring to a boil over medium heat, stirring constantly. Reduce heat to medium-low. Cook, without stirring, until a candy thermometer reads 250° (hard-ball stage).
Meanwhile, beat egg whites in a heat-proof large bowl until stiff peaks form. With mixer running on high speed, carefully add hot syrup in a slow steady stream, beating constantly at high speed for 5 minutes or until thickened. Cover and set aside.
In a large heavy saucepan, combine the remaining sugar, corn syrup and water. Bring to a boil over medium heat, stirring constantly. Reduce heat to medium-low; cook, without stirring, until a candy thermometer reads 290° (soft-crack stage).
Gradually pour hot syrup into egg white mixture; stir with a wooden spoon. Stir in the butter, vanilla and salt.
Pour mixture over peanuts in pan; press down evenly with buttered fingers.
For coating, in a large saucepan, combine the sugar, 1/2 cup cream and corn syrup. Bring to a boil over medium heat, stirring constantly; add remaining cream. Reduce heat to medium-low; cook and stir until a candy thermometer reads 242° (soft-ball stage).
Remove from the heat; stir in vanilla and salt. Pour over nougat layer in pan. Sprinkle with remaining peanuts, pressing slightly into nougat. Cool for at least 2 hours or until set. Cut into 1-1/2 in. x 1-in. pieces. Roll edges in additional peanuts and shape into logs. Wrap in waxed paper. Store at room temperature.