Preheat the oven to 350 degrees.
Divide beef into equal portions into patties. Salt and pepper on both sides.
On one patty, make a shallow well and place a piece of cheddar and mushroom in the center.
Cover with another patty and press to seal.
Heat a cast iron skillet over medium-high heat until hot but not smoking. Place patties in the skillet and brown on both sides. Remove skillet from stove top and place in the oven for about 25 minutes (depending on the thickness of your burgers) or until a thermometer reaches an internal temp of 160 degrees.
Serve on buns with your choice of toppings.