Line a mesh sieve with a coffee filter. Pour yogurt into sieve and allow yogurt to drain over a measuring cup in the refrigerator until about 1/2 cup whey is collected, about 8 hours.
Whisk half-and-half and drink mix in a large bowl. Add yogurt and sweetened condensed milk, stirring until smooth.
Pour into the container of an ice cream maker and freeze according to the manufacturer's instructions.
