Preheat oven (or toaster oven) to 350°F.
Heat skillet over medium heat. Melt 2 tablespoon butter, then add thinly sliced onions and stir until soft and translucent (2-3 minutes). Season with a pinch of salt and a few grinds of pepper. Reduce heat to medium low and continue stirring occasionally, about 20-30 minutes. NOTE: If the bottom of the pan begins to brown or burn as the liquid cooks away, add a splash of water or chicken stock as you stir and scrape the browned bits off. Those brown bits are full of flavor that the onions will reabsorb.
While onions cook, season the steak with salt and pepper.
Heat a large skillet (cast iron preferred) over medium-high heat. Add 1 tablespoon oil. When oil is shiny and coats the pan, cook steak to desired doneness. It's thin, so it will cook fast — approximately 4-6 minutes total. Remove from skillet and let rest 3-5 minutes on a cutting board.
Add thinly sliced peppers to onions in skillet. Stir occasionally to soften, approximately 7-10 minutes.
On a sheet tray lined with aluminum foil, arrange the two split ciabatta rolls so the insides are facing up. Spread the insides with butter or mayo (and whole grain mustard, if you're using it). On the bottom halves of the ciabatta rolls layer approximately ⅓ of the Havarti cheese. On the top halves, layer the remaining ⅔ cheese. Toast in the oven for 3-5 minutes until cheese is bubbly and melty. Remove the ciabatta from the oven. Layer the bottom half of each sandwich with the sliced steak and as much of the onion/pepper mixture as you want. Immediately close the sandwiches, pressing down so the melty cheese seals the bread together. Serve warm.