Pat steaks dry with paper towels and season both sides liberally with salt and pepper.
Heat olive oil in a large cast-iron skillet over medium-high heat until shimmering.
Place steaks in the skillet and sear for 4 to 5 minutes per side for medium-rare, or until internal temperature reaches 135°F (57°C). Remove steaks and let rest on a plate.
Wipe excess fat from the skillet and melt 1 tablespoon of butter over medium heat.
Add shrimp to the skillet in a single layer and cook for 2 minutes per side until pink and opaque. Remove shrimp and set aside.
Add the remaining 3 tablespoons of butter and minced garlic to the skillet; sauté for 1 minute until fragrant.
Pour in the heavy cream and oregano. Bring to a gentle simmer for 3 to 5 minutes until the liquid reduces and thickens slightly.
Stir in the parmesan cheese until completely melted and the sauce is smooth.
Return the steaks and shrimp to the skillet, spooning the cream sauce over the proteins to coat.
Garnish with fresh parsley and serve immediately.