Remove your ribeye steaks from the refrigerator about 20 minutes before you plan to cook them. Season with salt and pepper.
Heat olive oil in a large sauté pan and sauté the onions until browned and tender. Remove and repeat the process with the mushrooms, but do not remove from the pan. Add the onions to the sautéed mushrooms along with 1 teaspoon butter. Sauté until the butter is browned and sweet. Remove from pan. Add the wine and the sherry to the same pan and reduce the volume by one-half. Add chicken broth and reduce by one-half again. Add the mushrooms and onions and season with salt and pepper. Cover and leave over very low heat while you cook the steaks.
Set a large nonstick sauté pan over high heat until it is smoking hot. Lightly coat the bottom of the pan with canola oil and add the steaks, two at a time, or more if they fit comfortably. Do not crowd the pan. Sauté for 4-5 minutes per side for a medium-rare 12-ounce, 1 1/2-inch thick steak. Adjust time for the size of steak and desired doneness. Season with salt and pepper and serve with mushrooms and onions atop and alongside.