Line a large colander or sieve with 5 layers of dampened cheesecloth, allowing the cheesecloth to extend over outside edges of colander; place colander in a large bowl.
Heat buttermilk in a large, heavy saucepan over medium-high heat. Attach a candy thermometer to edge of pan so that thermometer extends at least 2 inches into buttermilk. Cook until candy thermometer registers 170 (about 20 minutes), gently stirring occasionally. Stir in juice. As soon as buttermilk mixture reaches 170 again, stop stirring (whey and curds will begin separating at this point). Continue to cook, without stirring, until thermometer registers 19
(Do not stir, or curds that have formed will break apart.) Immediately remove pan from heat. (Bottom of pan may be slightly scorched.) Using a slotted spoon, gently spoon curds into cheesecloth-lined colander; discard whey, or reserve for another use. Return colander to bowl; cover with plastic wrap. Refrigerate 8 hours or overnight.
Scrape cheese into a bowl.
Add chives, cilantro, parsley, salt, and freshly ground black pepper; toss gently with a fork to combine.
