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HEAT oven to 325°F oven.
MICROWAVE chocolate and butter in large microwavable bowl on HIGH 2 min. or until butter is melted. Stir until chocolate is completely melted.
STIR in sugar, eggs, 1 Tbsp. instant coffee and vanilla. Blend in flour; stir in nuts. Spread batter into 9-inch glass pie plate sprayed with cooking spray.
BAKE 25 min. or until toothpick inserted in center comes out with fudgy crumbs. (DO NOT OVERBAKE.) Cool completely on wire rack.
STIR remaining instant coffee into milk until dissolved. Beat pudding mixes and milk mixture in large bowl with whisk 2 min. Let stand 2 min. Spread over pie. Refrigerate 3 hours.