Heat a heavy skillet over medium heat, then add 1 tablespoon olive oil and one tablespoon butter to the hot pan. Add the onions, sautéing until they begin to color. Reduce heat to low, season with salt and pepper, and continue to cook, stirring occasionally, until deeply caramelized, about 40 minutes.
Heat a second heavy skillet over high heat. Rub 1 tablespoon olive oil over all surfaces of the rib eye, and season generously with salt. Sear the steak for 3 minutes per side, then transfer to a cutting board to rest for 8-10 minutes. While the steak rests, deglaze the pan with cognac, reduce by half, then add mustard and beef stock. Wisk pan sauce over medium heat until reduced to just a few tablespoons of liquid. Turn off the heat and add a tablespoon of butter.
When ready to serve, preheat a broiler. Split the baguette lengthwise, leaving a "hinge". Remove some of the crumb of the bread. Arrange the caramelized onions evenly over the bottom of the baguette. Thinly slice the steak and arrange on top of onions. Top with the shredded gruyere and broil just to melt cheese, about 30 seconds. Dress the arugula lightly with lemon juice and a pinch of salt, and arrange on top of melted cheese. Close the sandwich, cut in half, and serve warm.