Line a wire strainer with cheesecloth and set over a bowl. Pour the yogurt into the lined strainer and place in the refrigerator to drain for 6 hours or overnight. Once strained, place thickened yogurt in a bowl with the sugar, corn syrup, and vanilla bean paste. Stir until smooth. Pour into an ice cream maker and process according to manufacturer’s instructions, about 20–25 minutes. Spoon frozen yogurt into freezer-proof containers, press a piece of plastic wrap on top, and freeze to harden. After 4 hours, the frozen yogurt will still be soft but scoop-able. Once frozen 12–24 hours or more, you’ll want to leave it on the counter to sit for 5 minutes before scooping.