Bring 1 1/2 qts. water, the wheat berries, and 1/2 tsp. salt to a boil in a medium covered saucepan over high heat. Reduce heat and simmer until wheat berries are tender but not mushy (some should start to burst), about 1 1/4 hours. Drain.
Whisk 1/2 tsp. salt, the pepper, oil, 3 tbsp. vinegar, the paprika, and currants together in a large bowl. Let stand while wheat berries cook.
Cut brussels sprouts into fine shreds, preferably using a food processor with a slicing disk or a mandoline. Add brussels sprouts and wheat berries to dressing mixture and toss to coat. Taste and add more salt and another splash of vinegar if you'd like. Serve immediately.
Make ahead: Through step 2 up to 1 day, chilled. Bring to room temperature.
Note: Nutritional analysis is per serving.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.