Line a large sieve with 2 layers of cheesecloth or paper towels and set it over a large bowl.
Bring the milk, cream and 1 teaspoon salt to a simmer in a large nonreactive pot over medium heat, stirring occasionally. Add the lemon juice and vinegar and cook, stirring, until the mixture curdles, about 1 minute.
Pour the mixture into the prepared sieve and let drain, discarding the liquid (whey) from the bowl as necessary, at least 5 minutes or up to 30 minutes for thicker cheese. Store in an airtight container in the refrigerator for up to 4 days.