Prepare all ingredients. Heat a medium-sized saucepan over medium-low heat, add butter to the pan, lightly season with salt and toast the inside of the buns. (Be careful not to push the buns all the way flat into the pan until they have warmed slightly and are more pliable.) Reserve the toasted buns for later.
Turn the pan to medium-high and coat the inside lightly with oil. Add in mushrooms and lightly add salt and pepper, then cook until a slight amount of color forms on the edges. Add in sliced onions and peppers, again adding light salt and pepper. Keep moving and cook until onions and pepper start to soften (adding more oil as needed if the pan gets dry).
Add in more oil before adding the beef and season lightly with salt and pepper. Keep moving in the pan and, just before all of the pink is gone, add garlic.
Mix the vegetables and beef. Taste and adjust seasoning as needed.
Separate into four even piles and top with cheese. Turn off the heat and allow the cheese to melt, adding a lid to the pan if needed.
Portion the meat, vegetables and cheese onto the buns and serve.