Pat ribeye steaks dry with paper towels.
Season both sides, to taste, with salt and black pepper.
Pour 1 tablespoon olive oil into a medium skillet. Place over medium heat.
When oil is hot and shimmering, add steaks. Sear for 3 - 4 minutes per side, achieving a deep brown crust. Transfer steaks to a plate and tent with foil to keep warm.
In same skillet, add remaining 1 tablespoon of olive oil.
Add prepared garlic and onion. Sauté for 2 - 3 minutes until fragrant and translucent.
Add prepared mushrooms and red bell pepper. Cook for 5 minutes until softened.
Stir in crushed red pepper flakes and dried oregano. Cook for an additional minute.
Pour in dry white wine, scraping up any browned bits from the skillet. Allow the wine to reduce by half, about 2 - 3 minutes.
Add hand-crushed San Marzano tomatoes, Kalamata olives and capers. Stir to combine and bring the sauce to a gentle simmer. Cook uncovered for 15 - 20 minutes, allowing the flavors to meld and the sauce to thicken.
Return seared steaks and any accumulated juices to the skillet, nestling them into the sauce. Spoon some sauce over the steaks. Cover and simmer on low heat for 5-7 minutes, or until the steaks reach your desired doneness.
Remove the skillet from heat.
Stir in basil leaves, parsley and unsalted butter until the butter melts, enriching the sauce.
Plate the steaks with generous spoonfuls of the pizzaiola sauce.
Serve alongside cooked spaghetti or with slices of crusty bread to soak up the flavorful sauce.