Preheat oven to 425 °F. Prepare outdoor grill or grill pan to medium-high heat.
Unroll steaks on a large work surface and lightly pound if necessary to make the meat an even thickness, about ¼- to ½-inch thick. Drizzle meat with EVOO and season both sides with salt and pepper. Scatter the zest of 1 lemon on each steak. Halve the zested lemons for grilling and reserve. Top the meat with rosemary and chopped garlic, and scatter a layer of parsley over the top using about 1 cup of leaves per steak. Top the parsley with shaved Parmigiano-Reggiano cheese.
Carefully wrap and roll the steaks into large pinwheels. Tie the center of each steak tightly with butcher twine at the center then tie of 2 more pieces of string on either side of the center string, about 1 inch in from the edges. Cut each steak evenly, spacing your knife between the strings to form 6 pinwheels each about 1 ½ inches thick and 4 inches in diameter.
On a baking sheet, toss thin florets of broccoli with salt, pepper, crushed red pepper, sliced garlic and red peppers, and dress with just enough EVOO to coat. Roast 15-18 minutes until crispy at edges and just tender.
Brush or spray grill with canola or olive oil and grill the meat about 8 minutes turning once or until desired doneness. Grill lemon halves cut-side down for 2-3 minutes to caramelize.
Douse pinwheels with grilled lemon juice and serve with a pile of roast broccoli alongside.