While the potatoes are roasting, prepare the blue cheese filling: Combine rosemary, blue cheese and lemon zest in a small mixing bowl. Season the filling with salt and pepper and set aside.
For the steaks, place them wide side down on a table and bracing it with your hand. Using a very sharp knife, cut a slit into the side of each steak, creating a pocket that still leaves the two halves attached. Divide the filling evenly among the four steaks, spreading it evenly inside each pocket and sealing the steak opening closed with a few toothpicks. Drizzle each steak with some olive oil, salt and freshly ground black pepper and toss them lightly to evenly coat them, then set them aside at room temperature until you're ready to cook them off.
After the potatoes have been roasting for 25 minutes, place a large skillet or cast iron pan over medium high heat. When the pan is scorching hot, place each steak into the pan and allow them to sear on both sides, turning only once, until well caramelized, 3-4 minutes per side.
While the steaks are searing on the stovetop, place the broccoli on a baking sheet and coat it in a light drizzle of olive oil. Season it with salt and freshly ground black pepper and reserve.
Once both sides have been seared, transfer the pan with the steaks and baking sheet of broccoli to the oven alongside the potatoes. Roast the broccoli until golden brown and tender, about 10 minutes. Allow the steaks to continue cooking until your desired doneness, about 10 minutes for medium (if your skillet isn't oven safe or you're not comfortable putting your pan into the oven, transfer the steaks to a small baking sheet and place them into the oven on that).