Pat the steaks dry, brush them with the oil, and season evenly with the salt and pepper. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Meanwhile, bring a large pot of salted water to a boil. Add the spinach and cook just until wilted, about 1 minute. Transfer to a large colander and drain extremely well, pressing firmly on the spinach, or wrap in a clean kitchen towel and squeeze to remove as much excess liquid as possible. Coarsely chop the spinach and set aside.
In a large skillet over medium-low heat, melt the butter. Add the shallots and garlic and cook until very tender, 7 to 8 minutes, stirring occasionally. Add the flour and cook until golden brown, about 1 minute, stirring constantly. Increase the heat to medium; gradually add the half-and-half and stir until the mixture thickens, 2 to 3 minutes. Stir in the spinach and nutmeg and cook until heated through, 1 to 2 minutes. Remove from the heat, add the cheese, and stir until melted. Cover to keep warm.
Grill the steaks over direct high heat, with the lid closed, until cooked to your desired doneness, 8 to 10 minutes for medium rare, turning once or twice. Remove from the grill and let rest for a few minutes. Serve warm with the Gorgonzola creamed spinach and crusty bread or French fries, if desired.