Line an 8x4x2-inch loaf pan with foil, extending foil over edges of pan. Butter the foil; set pan aside.
Butter side of a heavy 2-quart saucepan. Combine granulated sugar, brown sugar, and half-and-half or light cream in saucepan. Cook and stir over medium heat until mixture boils. Clip a candy thermometer to side of pan. Reduce heat to medium-low; continue boiling at a moderate, steady rate, stirring frequently, until thermometer registers 236 degrees F, soft-ball stage (about 15 minutes). Adjust the heat as necessary to maintain a steady boil.
Remove saucepan from heat. Add butter and vanilla, but do not stir. Cool mixture, without stirring, to 110 degrees F (about 40 minutes).
Remove thermometer from saucepan. Beat mixture vigorously with a clean wooden spoon until fudge just begins to thicken. Add nuts. Continue beating until fudge becomes thick and just starts to lose its gloss (about 10 minutes total).
Spread fudge immediately into the prepared pan. Score into squares while warm. When fudge is firm, use foil to lift it out of pan. Cut fudge into squares. Store in a tightly covered container. Makes about 1-1/4 pounds (32 servings).