Scoop the avocados into a small mixing bowl and use the back of a fork to mash the avocado. Season with salt and set aside. Cut the halloumi in half lengthwise.
Fry the cheese
Heat a medium nonstick skillet over medium high heat, add 2 tablespoons of vegetable oil and place the cheese in the pan. Cook until the cheese is golden brown, about 1 min.
Flip the cheese
Flip the pieces and repeat on the other side, cooking for about an additional 1 minute. Remove and set aside, then return the pan to heat.
Cook the eggs
Add the remaining oil and heat, then crack the eggs in the pan. Cook until the whites set, about 1 min. Gently break the yolk and flip the eggs, cooking for an additional 30 seconds for over easy.
Toast English muffin
Return the pan to heat, add butter and melt. Add the english muffins to the pan, cut-side down. Toast until golden brown, about 2 minutes. Remove and set aside.
Assemble and serve
Divide the smashed avocado between the two bottoms of the sandwich, then top with the crispy halloumi slices, fried eggs followed by the arugula and hot sauce. Close and serve.