In a large bowl, combine all of the ingredients except for the beef stock, butter, cream of mushroom soup, garlic, Worcestershire sauce, mushrooms and sour cream.
So in your bowl you should have: meat, crackers, milk, onion, green pepper, all your seasonings and herbs.
Combine the meat, crackers, eggs, onions, green peppers, milk and seasonings until they are WELL combined.
Next, you want to form large patties. These patties will be more wet than your usual meatballs or hamburgers. Prepare a cookie sheet with foil and make about 10 patties that are about the size of your hand and about 2� thick.
This step is KEY. You must allow the patties to rest at room temp for about 30 minutes. This is so they have time to bind. As I said, they will be more wet than your typical meatball or ground meat recipe.
When your patties have rested for about 30 minutes you want to heat 2 to 3 T of butter in a deep skillet. When the butter is warm, add your garlic cloves and give it a swirl in the butter.
Prepare a plate with paper towels to keep near the stove where you will be frying your patties.
Carefully remove 2 or 3 patties and place them in your skillet. Allow the patties to cook for about 5 to 7 minutes on the first side before flipping. You want to get a nice sear on each side.
When they are well seared on both sides, remove them from the skillet and place on the prepared paper towel dish. Fry the rest of your burgers until they all have a good sear.
When you are done frying all the burgers, add the rest of the butter and then add the mushrooms to the hot skillet. Allow the mushrooms to brown and add the Worcestershire sauce. Use a spatula to scrape up the meaty bits from the bottom of the pan as the Worcestershire sauce loosens them.
Give your mushrooms about five minutes to simmer in the Worcestershire sauce.
Next add the beef broth and cream of mushroom soup and whisk until smooth.
This is the step you add your burgers BACK to the pan of gravy you just made. They should have shrunk while cooking so you should have room for them all. Make sure they are submerged in the gravy and bring the pan to a simmer.
Reduce heat, cover with a lid and allow to simmer for 30 minutes.
At the thirty minute mark, make room in the center of the pan, and add your heaping spoon of sour cream and whisk until combined into all of the gravy.
Serve your hamburgers on top of mashed potatoes and top with gravy and a sprinkle of dill.