Line an 8-in. square pan with foil; grease foil with 1 teaspoon butter.
In a large heavy saucepan, combine remaining butter, granulated and brown sugars, cream 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 to pan (do not stir).
Cool, without stirring, to 110°, about 30 minutes. Beat with a spoon until fudge just begins to thicken. Gradually stir in confectioners' sugar until smooth; add nuts and continue stirring until fudge becomes very thick and just begins to lose its sheen. 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 an airtight container.