Place butter in a small pot and add the flour to make a roux. Gently cook for three to four minutes making sure not to burn.
Whisk in the cold milk until there are no lumps. Bring to just under a boil and cook until sauce starts to thicken.
Remove from heat, and whisk in the mustard and cheeses. Set in a warm place.
Heat large cast iron skillet on medium–high. Get the butcher to thinly slice your meat. Or freeze until firm; slice thinly across the grain. Season the meat with salt and pepper.
Cook quickly with a tablespoon of olive oil until medium-rare. Remove meat to a bowl toss with as much beef vinaigrette as desired, keep warm.
In the same pan add first the onions cook for three minutes then add the garlic and peppers.
Cook for another two minutes then add the mushrooms. Sauté quickly and season with salt and pepper.
To dress the sandwich, quickly warm through the ciabatta bun and slice in half. Add the warm dressed beef and the onion, mushroom mix. Top with a generous amount of cheese dressing and onions or jalapeño.