Whisk Creamy Tarragon Sauce ingredients together and set aside in the refrigerator.
Form the meat into 7-ounce patties. Submerge them in a bowl of ice water for 30 seconds. Immediately transfer the burgers to a hot grill and brush with melted butter. Grill over high heat for 9 minutes for medium-rare, turning several times and occasionally brushing with butter. Top the burgers with a slice of grass-fed Cheddar cheese toward the last minute or two of grilling. Assemble your condiments, including the Creamy Tarragon Sauce, and kick back and enjoy.