Pre-heat the oven to 425°F. Prepare the outdoor grill or grill pan to medium-high heat.
Unroll the steaks on a large work surface and lightly pound, if necessary, to make the meat an even thickness, about a quarter to one-half inch thick. Drizzle the 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 off two 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 six pinwheels, each about 1 1/2 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 for 15-18 minutes, until crispy at the edges and just tender.
Brush or spray the grill with canola or olive oil and grill the meat for about 8 minutes, turning once or until desired doneness. Grill the lemon halves cut-side down for 2-3 minutes to caramelize.
Douse the pinwheels with grilled lemon juice and serve with a pile of roast broccoli alongside.