Heat 1 tablespoon of olive oil and 1 tablespoon of butter in a large heavy-bottomed skillet over medium-high heat.
Add sliced onions and quartered mushrooms to the skillet.
Stir continuously for 3 to 4 minutes until vegetables are golden brown and liquid has evaporated.
Add marjoram, rosemary, and salt to the vegetables and cook for one additional minute.
Remove the vegetable mixture from the skillet and set aside in a bowl.
Wipe the skillet clean if necessary and return to medium-high heat.
Add the remaining olive oil and 1 tablespoon of butter.
Sear the steak strips in batches to avoid crowding the pan, cooking until browned to your desired doneness.
Add the remaining butter and minced garlic to the pan, tossing the steak for 30 seconds until fragrant.
Return the cooked mushrooms and onions to the skillet.
Season with pepper, toss everything together to coat in the garlic butter, and serve immediately.