Place a sieve over a bowl and line the sieve with two layers of cheesecloth. Pour 1 quart plain whole-milk yogurt into the cheesecloth and fold the edges over the yogurt to cover. Set the yogurt in the refrigerator for 3-4 hours until a cup of liquid has drained from the yogurt.
Discard the liquid and put the yogurt into the bowl. Stir in 4 oz sugar, 3 oz honey and vanilla bean seeds. Let the mixture sit for 15-20 minutes in the refrigerator until all the sugar has dissolved.
Run the mixture in your ice cream machine according to the manufacturer's instructions.
Transfer the frozen yogurt to a plastic container and lay a piece of plastic wrap directly on the surface of the yogurt. Cover the container and freeze at least 6-8 hours until solid. (see note)
Notes
Because of the honey this yogurt will not freeze rock-hard. It will be scoop-able right out of the freezer.