Place steak in a single layer in a baking dish or shallow heatproof bowl. In a medium saucepan, combine wine, red wine vinegar, shallot and rosemary; bring mixture just to a boil, then pour over steak. Marinate steak, turning once, until liquid is cooled, about 20 minutes. Meanwhile, prepare purée.

In a small saucepan, combine 1/4 cup plus 1 tablespoon oil and garlic. Heat over medium-high heat 2 minutes, then remove from heat. Stir in white wine vinegar and 1/4 teaspoon salt (oil will bubble up a bit); let stand 10 minutes.

In the bowl of a food processor, combine artichokes, olives, parsley, basil, zest and generous pinch salt. Add warm oil mixture; purée until smooth. 

Remove steak from marinade; discard marinade. Pat dry steak, then season with salt and pepper. In a large cast iron or heavy skillet, melt butter with remaining tablespoon oil over medium-high heat. Cook steak 3 minutes then turn, reduce heat to medium and cook 5 minutes more for medium-rare. Transfer to a large plate; let rest 10 minutes. Reserving juices, transfer steak to a cutting board. Against the grain, cut into 4 portions.

Spread about 2 tablespoons artichoke purée on each of 4 serving plates; arrange spinach on top. Drizzle greens with oil and season with salt; arrange steak on top. Drizzle juices and spoon remaining purée over steaks.