Bring a large pot of water to a boil over high heat; generously salt water and return to a boil. Add herbs and cook for 30 seconds. Drain and rinse under cold running water.
Place herbs on a cutting board and mince. Transfer to the jar of a blender with ice cube and cold water; blend, starting on low speed and working up to high until smooth. Scrape down sides and blend 20 to 30 seconds more, scraping down sides again if necessary.
Transfer herb mixture to a small saucepan and place over medium-low heat. Whisk in butter, 1 piece at a time, and season with salt and pepper. Keep warm until ready to use.