Making it up to the kids (french hamburgers to make up for last night's pig pie)

This is basically the same recipe (from Mastering the Art of French Cooking) as the bifteck hache a la lyonnaise.   It is Bitokes a la Russe (Hamburgers with Cream Sauce):  The patties are made with one pound ground beef, 3/4 cup minced onion sauted in 2 tbsp butter for 10 minutes, 1 1/2 tsp salt, ground pepper, 1/4 tsp dried thyme, and one egg. ( I left out the extra 2 tbsp butter.  I think my beef was fatty enough)  Make 4 patties and dredge in flour.  Cook patties in 1 tbsp butter and 1 tbsp olive oil until med rare.  Keep warm.  Pour fat off of pan.  Add 1/4 beef broth and boil until syrupy.  Add 2/3 cup cream and boil.  Add salt, pepper, pinch of nutmeg and a couple drops of lemon juice.  Turn heat off.  Swirl in 2-3 tbsp butter 1/2 tbsp at a time.  (We stopped at 1 tbsp)  Stir in 2 tbsp minced parsley.  We served it with olive oil mashed potatoes and steamed broccoli.