Over medium heat, add the two tablespoons of olive oil to a medium pan. Add in the sliced onions, salt and pepper to taste and continue stirring until the onions are rich and caramelized, about 20 minutes. Remove the onions from the pan, and set them aside.
Toast four sliced of bread to your desired darkness. Once the toast is done, slather one side of all four pieces with the herbed butter.
In the same pan that you used for the onions, drop in the steak over medium high heat and toss continuously until the steak is warmed through.
Assemble the sandwich starting with the steak, followed by the onions and arugula.