Line a 9-in. square pan with foil; grease foil with 1 teaspoon butter., In a large heavy saucepan, combine sugars, milk, corn syrup and salt. Bring to a rapid boil over medium heat, stirring constantly. Cook, without stirring, until a candy thermometer reads 234° (soft-ball stage). Remove from heat. Add vanilla and remaining butter to pan (do not stir)., Cool, without stirring, to 110°, about 40 minutes. Beat with a spoon until fudge just begins to thicken. Add walnuts; continue beating until fudge becomes very thick and just begins to lose its sheen (about 10 minutes total). Immediately spread into prepared pan. Cool., Using foil, lift fudge out of pan. Remove foil; cut fudge into 1-in. squares. Store between layers of waxed paper in airtight containers.