Cut the cheeses into ½-inch chunks or smaller. Place in a food processor along with the garlic. Season with pepper. Pulse to break cheese up into small bits.
To food processor, add the butter and herbs. Pulse to combine. Pulse in the wine 1 tbsp at a time, until mixture is spreadable but not runny, stopping and scraping side of bowl occasionally. Serve immediately with crackers, toast, or vegetables, or transfer to an airtight container and refrigerate up to 1 week. Let stand at room temperature 10 min. before serving.
No wine? Use 2–3 tbsp milk mixed with a squeeze of lemon juice instead.