Add all of the ingredients for the Salisbury steaks, other than the butter or olive oil, to a large bowl. Combine the mixture with your hands until fully incorporated, then shape into 5 patties.
Add the butter to a large skillet over medium heat. Once sizzling, place the patties in the pan. Cook for 5-6 minutes, until browned, then flip and cook for an additional 5 minutes, until browned, and remove from the pan.
Add another tablespoon of butter to the pan. Once melted, add the mushrooms, onion, and garlic. Cook for 7-8 minutes, until the mushrooms and onions, are browned and starting to caramelize.
Sprinkle the flour over the mushrooms and onions and whisk to combine. Then, pour in the beef broth, whisking constantly, until smooth. Let the gravy come to a bubble, then reduce the heat to low.
Stir the heavy cream, thyme, salt, and pepper into the gravy, then transfer the patties back to the pan and cover with the sauce. Cook for about two minutes to heat them back up, then serve over mashed potatoes or another side of choice.