Pat the steak dry with a paper towel. Season the steak generously with salt, then let it rest at room temperature for 40 minutes or up to 2 hours.
Heat a medium stainless-steel or cast-iron skillet over high heat until very hot. Pat the steaks dry with paper towels again, then season the steaks with pepper.
Add half of the olive oil to the pan, then add the steak and sear until is nicely browned on the bottom, checking after 1 minute and searing up to 3 minutes. Repeat on the other side, then continue cooking the steak, flipping with tongs every 1 minute, until the internal temperature has reached 110°F (43°C) for rare, 120ºF (49°C) for medium-rare or 130°F (54°C) for medium (steak will continue to cook for a bit once removed), 6 to 10 minutes depending on thickness. Remove the steak from the skillet, tent loosely with foil, and let it rest for 10 minutes.
Meanwhile, make the mushroom red-wine sauce: Using the same skillet set over medium-high heat, add one-third of the butter, half of the shallot, and all of the mushrooms and cook, stirring occasionally, until the mushrooms have released their liquid and shallots are browned, 4 to 5 minutes. Add the red wine, then keep at a boil, stirring often until reduced and syrupy, 2 to 3 minutes. Add half of the broth and bring it to a boil, stirring often, until reduced by about one third. Remove the skillet from the heat and whisk in half of the remaining butter. Season the sauce with salt and pepper to taste.
Make the creamed spinach: In a clean skillet, melt the remaining butter and olive oil over medium heat. Add the remaining shallots and a pinch of salt. Cook until shallots are softened, about 3 minutes. Stir in the cream cheese, heavy cream, and remaining broth; cook, stirring, until cream cheese is melted and smooth. Stir in the spinach; add the nutmeg and cayenne pepper and simmer over medium heat, stirring until spinach wilts and mixture thickens, 3 to 4 minutes. Remove from the heat and season with salt and pepper.
Slice the steak, divide it among dinner plates, top the steak with the sauce, and serve with the creamed spinach on the side.