Philly Steak and Grilled Cheese

For the Steak:

flank steak, still partially frozen (see note)

Worcestershire sauce

oil

coarse ground black pepper

kosher salt

very thinly sliced onion

very thinly sliced bell peppers

button mushrooms, sliced

For the Cheese Sauce:

unsalted butter

COLD milk

cornstarch

shredded Horseradish Cheddar (or sharp white)

For the Sandwiches:

butter for the skillet

slices sourdough bread