In a large skillet over medium-high heat, melt butter together with olive oil.
Add the chopped onion and minced garlic. Sauté for about 2–3 minutes until the onion becomes soft and translucent.
Add the sliced mushrooms and cook for about 5 minutes until tender and slightly browned.
Stir in the thinly sliced steak and pesto sauce. Mix well so the steak absorbs the flavors.
Season with salt and pepper to taste.
Pour in the beef broth and white vinegar, then add the heavy whipping cream. Stir well.
Reduce heat to low and let the sauce simmer for 10–15 minutes until it thickens slightly.
Meanwhile, bring a large pot of salted water to a boil. Cook tortellini according to package instructions until al dente.
Drain the pasta and add it directly to the skillet with the sauce.
Toss everything together and simmer for another 5 minutes so the Steak Mushroom Tortellini absorbs the creamy sauce.
Garnish with shaved Parmesan and fresh basil before serving.