Grease large cookie sheet (17 x 11 inches).
Combine sugar, water and corn syrup in heavy-bottomed 3-quart saucepan. Cook, stirring occasionally, over medium-high heat until temperature registers 275 degrees F on candy thermometer, or soft-crack stage, about 20 minutes (mixture forms pliable strands when drizzled from a metal spoon).
Stir in the cashews. Continue cooking, stirring occasionally to prevent the nuts from scorching, until the temperature reaches 305 degrees F, or hard-crack stage, 5 to 7 minutes longer (mixture will be amber-colored and, when dropped into ice water and removed and bent, will snap). Remove the saucepan from the heat. Quickly stir in the vanilla and the baking soda.
Pour onto prepared cookie sheet, pushing brittle to edges of sheet with back of wooden spoon. As candy cools, stretch it out thinly by lifting and pulling from edges, using 2 forks. When brittle is completely cooled, loosen from sheet; break into pieces.
Store in airtight container at room temperature for up to 1 month.