Add onions and parsley and cook gently 3 minutes, stirring constantly (do not let onions brown).
Add tarragon, lemon juice, wine, 3/4 tsp. salt and 1/8 tsp. pepper.
Bring to a boil, turn down heat and simmer 3 minutes.
Combine ground beef, 1 1/2 tsp. salt and 1/4 tsp. pepper, mixing lightly.
Divide meat into 6 and pat lightly into 6 large thick patties.
Set on greased grill or in broiler basket and broil over hot coals until done the way you like them, brushing with onion sauceoften.
Keep sauce hot and serve any remaining with the hamburgers.