Put the yogurt into a yogurt drainer (e.g., the Wave); or divide it among several paper coffee filters set into a strainer or attached to the top of cups with rubber bands.
Put the yogurt in the refrigerator, covered, and let it drain for 24 hours; you'll end up with about 2 cups of thick yogurt. Note: Don't feel like draining regular yogurt? Simply use 2 cups thick Greek-style yogurt; no need to drain it.
While the yogurt is draining, put the bucket of your electric ice cream maker into the freezer to chill.
Combine the drained yogurt with the remaining ingredients.
Freeze in your ice cream maker according to the manufacturer's directions.
Serve immediately, drizzled with a touch of vanilla extract, if desired. Or store in the freezer briefly before serving. This confection will freeze rock-hard within hours; if you need to make it ahead, be sure to leave time for it to soften before serving, about 15 minutes. Also, check out the tip at left for keeping frozen yogurt soft and scoopable in the freezer indefinitely.