Line an 8 x 4 x 2-inch loaf pan with foil, extending foil over edges of pan. Butter foil; set pan aside.
Butter sides of a heavy 2-quart saucepan. In pan combine sugar, milk, half-and-half, and corn syrup. Cook and stir over medium-high heat till mixture boils. Clip a candy thermometer to pan. Reduce heat to medium-low; continue boiling at a moderate, steady rate, stirring frequently, till thermometer registers 238 degrees F, soft-ball stage (25 to 35 minutes).
Remove saucepan from heat. Add butter and vanilla, but do not stir. Cool, without stirring, to 110 degrees F (about 55 minutes).
Remove thermometer from saucepan. Beat mixture vigorously till fudge becomes very thick and just starts to lose its gloss (about 10 minutes total).
Immediately spread fudge in prepared pan. Score into squares while warm. When firm, use foil to lift it out of pan. Cut fudge into squares. Store tightly covered. Makes about 1 pound (32 pieces).