Halve cucumber lengthwise, then thinly slice crosswise. Thinly slice cabbage and red onion (a food processor fitted with the slicing blade would work nicely or a mandoline.) Combine cucumber, cabbage, and onion in a bowl. Bring remaining ingredients to a boil in a saucepan, stirring, and immediately pour over cucumber mixture. Toss mixture and let stand at room temperature, stirring occasionally, about 10 minutes. To cool quickly, chill in freezer for 15 minutes.;