Line a 9-in. square baking pan with foil. Grease foil with butter; set aside.
Combine milk and chips in a large microwave-safe bowl. Microwave, uncovered, on high for 1 minute; stir. Cook 30-60 seconds longer, stirring every 30 seconds, or until chips are melted. Stir in 1-1/4 cups candy canes and vanilla.
Transfer to prepared pan. Sprinkle with remaining candy canes; press down gently. Cover and refrigerate for 2 hours or until firm. Lift fudge out of pan using foil. Gently peel off foil; cut fudge into 1-in. squares. Store in an airtight container.