Season steak medallions with salt and black pepper on both sides.
Heat olive oil in a large skillet over high heat. Add steaks and cook until browned, about 2 minutes per side. Transfer to a plate. Reserve oil in skillet.
Place mushrooms and butter into the skillet and season with salt; cook and stir until mushrooms are softened and beginning to brown, 5 to 6 minutes. Reduce heat to medium; add peppers and cook and stir until softened, about 2 minutes. Stir in garlic and cook for 1 minute. Pour in wine and sprinkle in dried oregano. Increase heat to medium-high and cook until the wine is nearly evaporated, about 3 minutes.
Stir tomato concasse into the mushroom mixture and simmer until tomato is softened, 3 to 4 minutes. Add fresh oregano, balsamic vinegar, and red pepper flakes; stir to combine. Adjust salt and black pepper to taste.
Place steaks back into the skillet with the mushroom mixture and cook until warmed through and cooked to desired doneness, 4 to 10 minutes.