Make pickled onion: In a medium saucepan, heat sugar, rice vinegar, 1 cup water, and the salt, stirring occasionally, until sugar dissolves and mixture is steaming. Put onion and currants in a nonreactive bowl and pour liquid on top. Let stand at least 2 hours (chill, covered, if longer than that, up to 1 day).
Make cauliflower: Preheat oven to 350°. Break cauliflower into small florets and set on a rimmed baking sheet. Toss with oil and season with salt (pan will be full). Roast until golden, 45 to 50 minutes.
Make yogurt: In a medium bowl, whisk yogurt, vinegar, garlic, and salt to taste.
Spoon yogurt onto one or two platters and spread thin. Arrange cauliflower on top. Using a slotted spoon, lift onion and currants from liquid and scatter over cauliflower. Sprinkle with cilantro.
*Find brands of sugar cane vinegar (a mild, sweet-tasting vinegar) such as Datu Puti Sugarcane Juice Vinegar at Asian markets and amazon.com. Or substitute a bit less of Champagne vinegar.
Make ahead: Pickled onion and currants, up to 1 day, chilled.