Briefly toast the crostini crackers on each side in hot olive oil in a skillet until glistening and crisp. Remove and set aside.
Preheat a cast-iron skillet over medium-high heat.
Sprinkle the steak with salt and pepper, then rub with the mustard. Add the butter and 2 tablespoons olive oil to the skillet. Once the butter is melted, sear the steak until cooked to your preference, 3 to 5 minutes per side for medium rare. Allow to cool completely, then wrap in plastic wrap and chill. (This can happen anytime before.)
When ready to build the crostini, thinly slice the steak against the grain. Press a wedge of Brie on each crostini. Top with the sliced steak, peppers, parsley and shaved Parmesan.