Blanch the asparagus in boiling salted water for 60 seconds, and then run under cold water or place in an ice bath to stop the cooking process. Set aside.
Season the rib-eye steaks with salt and pepper on both sides and then cook by grilling or pan searing to desired doneness. Use an instant-read thermometer to check the internal temperature, 125 F for medium-rare, and let the steaks rest for 3 to 5 minutes before serving.
Heat a sauté pan or saucepan over medium-high heat and add 1 tablespoon of olive oil. Add the shallots and garlic and cook for 1 to 2 minutes, stirring frequently to avoid burning. Add the mushrooms and sauté until they soften and begin to brown. Add half of the bleu cheese crumbles, then add the bone broth and let it come to a strong simmer. Remove pan from the heat and add the arugula, turning over in the pan to coat evenly.
Divide the mushroom and arugula mixture between two plates. Return the pan to the stove and heat the other tablespoon of olive oil over medium heat. Add the cooled and drained asparagus and sauté for 30 to 60 seconds to heat through. Lay the steaks on top of the mushroom mixture, divide the asparagus between the two plates, and top the steaks with a sprinkle of remaining bleu cheese.