For the braciole: Put the flank steak in the freezer for 20 minutes to firm up for easy slicing.
Bring a pot of water to a boil and prepare an ice water bath. Blanch the asparagus briefly, then transfer them to the ice water to stop the cooking process. Drain and pat dry.
In a bowl, mix together the breadcrumbs, chiles, pine nuts, raisins, olive oil and garlic. Season with salt and pepper.
Butterfly the steak horizontally (the striations and grain should run horizontal at the end), opening the top flap like a book until it is one flat piece. Gently pound out with a meat mallet to even the thickness. Season both sides with salt and pepper.
Layer the cheese over the steak, leaving about a 1-inch perimeter. Then add the breadcrumb mixture and spread it within 1 inch of the edge, patting it down evenly. Next, horizontally layer the asparagus in the same fashion.
Starting at the shorter end of the steak (the striations and grain of the meat should be running horizontally), tightly roll the steak into a pinwheel, taking care to make it even. Using twine, tightly tie the roll in 1-inch increments, then loop around the edge to seal the sides.
Heat one side of a gas grill on high for indirect cooking.
For the braciole baste: Combine the olive oil, salt, pepper, garlic and oregano in a small bowl and mix together.
Season the exterior of the braciole with salt and pepper. Brush with the baste and sear on all 4 sides until properly browned, about 2 minutes per side. Lower the heat to medium and move the braciole to the cool side of the grill. Cover and cook, basting every 5 minutes with the braciole baste, until the internal temperature hits 120 degrees F, 40 to 45 minutes. Tent with foil and let rest for at least 15 minutes.
For the braciole sauce: This can be done directly on the grill while the braciole is resting. Heat a large, cast-iron skillet over medium-high heat. Add the olive oil and tomatoes. Give a toss, then don't move the tomatoes until they start to char and blister, 3 to 4 minutes. Toss again and finish charring for about 3 minutes. Pour into a bowl, toss with the basil and vinegar and season with salt and pepper. Stir until slightly broken and chunky.
Remove the string from the braciole, then slice into 1-inch medallions. Serve with the braciole sauce.