Cook pasta in a large pot of boiling salted water according to package directions until al dente. Reserve 1/2 cup of pasta water, then drain.
Season steak strips with salt and pepper.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Sear steak strips in batches for 2-3 minutes until browned. Remove steak from skillet and set aside.
Lower heat to medium and add remaining oil and butter to the skillet. Sauté minced garlic for 1 minute until fragrant.
Deglaze the skillet with beef broth, scraping the bottom to release browned bits.
Stir in heavy cream and oregano. Simmer for 3-4 minutes until the sauce thickens slightly.
Whisk in Parmesan cheese until melted and smooth.
Add baby spinach to the sauce and stir until wilted.
Return the steak and cooked pasta to the skillet. Toss to combine, adding reserved pasta water as needed to reach desired sauce consistency.
Adjust seasoning with salt and pepper to taste and serve immediately.