For spice rub: Mix paprika, black pepper, ancho powder, salt, sugar, coriander, thyme, garlic powder, and onion powder in a small bowl.
For stuffing: Crush bread into crumbs in a food processor, about 1 minute. You should have about 1 1/2 cups crumbs.
Heat 1 tablespoon of oil in a large nonstick skillet over medium heat. Add onion, garlic, and mushrooms, and cook until mushrooms shrink slightly, about 5 minutes. Add spinach, cover, and cook until spinach wilts, 2 to 3 minutes. Remove from heat and stir in bread crumbs, parsley, and 2 teaspoons of spice rub.
Preheat oven to 500ºF.
Position the steak on a large cutting board with rough side of meat facing up. Cut through the side of the steak to open it up like a book. Use a sharp, thin knife and start by making small slashing cuts from one short side to the other, lifting the top of the steak as you cut and always keeping the knife horizontal with the cutting board. Stop cutting just before reaching the opposite side and open up the steak so it lays flat (aka, butterflied).
Stand facing butterflied steak with the grain of the meat running from side to side. Gently pound steak to an even thickness of 1/4 to 1/2 inch. Rub all over with remaining 1 tablespoon of oil. Season all over with remaining 1 tablespoons of spice rub. Reposition so that cut side is up and grain is running from side to side.
Lay stuffing over steak, leaving a 1-inch border at the side furthest from you (the top). Roll steak from bottom to top into a compact roast. Using kitchen string, tie the roast crosswise at 2-inch intervals so it holds its shape.
Put a roasting rack on a roasting pan or sheet pan and set roast on the rack with seam side down. Roast until meat is lightly browned all over, 8 to 10 minutes total. If your oven has convection, turn it on to help brown the roast. Reduce oven temperature to 350ºF and roast until meat registers an internal temperature of 130ºF, 20 to 25 minutes total.
Remove to a cutting board and let stand for 15 minutes. Cut crosswise across the grain into slices about 1/2 to 3/4 inch thick, removing the string as you go.
Tip: Butterflying a flank steak is a simple process of cutting it open like a book to make it thinner. If your flank steak is less than 1/2-inch thick, skip the butterflying step and just pound it to 1/4-inch thickness. The steak will have slightly less total area, so you will need slightly less filling.