Combine all the ingredients for the blackening spice mix in a bowl. Set aside.
Heat the butter in a large skillet over medium heat. Add the mushrooms and the shallot, and cook for about 5 minutes until they are golden and fragrant. Pour out of the skillet into a large mixing bowl and let cool for a few minutes. Meanwhile, give your skillet a quick rinse and wipe it out with a paper towel.
Add your ground beef to the bowl with your cooked mushroom mixture. Mix with your hands until just combined, then form into five patties. Coat each side of the patties with your blackening spice mixture (you can just dip each side into the bowl with the spice blend).
Heat your skillet again over medium heat. Coat the pan with a little cooking spray. Add your patties to the pan, and cook for about 3-4 minutes per side, or until they reach an internal temperature of 165 degrees. Top with blue cheese crumbles and set them aside for a minute.
While the burgers are cooking or when they are done, toast your English muffins.
When the burgers have just finished, heat another skillet over medium heat. Give it a quick shot of cooking spray, and add your eggs. Cook them over easy – or as you desire.
Add a burger patty to each English muffin and top with your egg, arugula, and sliced tomato. Enjoy!