In a 10-inch skillet, melt the butter and 1 Tbs. oil over medium high heat until the butter melts, then add the onion and sauté until the onion turns golden brown, 1 to 2 minutes. Add the panko and garlic, and cook for another minute. Remove from the heat, then add the basil, ½ tsp. salt, and ¼ tsp. pepper. Stir to combine.

Place a rack in the center of the oven and heat the oven to 375°F. Line the bottom of a large roasting pan with aluminum foil.

Lay the flank steak on a large cutting board so that the grain runs from side to side, cover with plastic wrap, pound to ¼-inch thick, and spread the mixture evenly over the surface of the steak, leaving an inch around all edges. Top with the artichokes, peppers, and grated cheese, then roll the steak and secure with kitchen string every 2 inches. Season the steak all over with salt and pepper. Heat the remaining 2 Tbs. oil in a 12-inch skillet over medium-high heat until shimmering and add the steak, searing all over until deep golden brown on all sides, 1 to 2 minutes per side, adding more oil if needed, a total of 6 to 8 minutes. Transfer the steak seam side down to a rack in a large roasting pan. Roast until the internal temperature reaches 135°F for medium rare, about 35 to 40 minutes. Remove the roast from the oven, lightly tent with aluminum foil, and allow to rest for 10 minutes before slicing.