Philly Cheeseburgers

Prepare the grill for direct cooking over medium-high heat (400° to 500°F) and preheat a perforated grill pan over direct heat for about 10 minutes. Mix the ground chuck, 1 tablespoon of the oregano, 1 teaspoon of the salt, 1 teaspoon of the pepper, and the garlic, and then gently form four patties of equal size, each about ¾ inch thick. With your thumb or the back of a spoon, make a shallow indentation about 1 inch wide in the center of the patties to prevent them from forming a dome as they cook. Refrigerate the patties until ready to grill. Combine the onion, bell peppers, 2 tablespoons oil, the remaining ¾ teaspoon salt, the remaining ½ teaspoon pepper, and the crushed red pepper flakes and toss to coat. Spread the vegetables in a single layer on the grill pan and grill over direct medium-high heat, with the lid closed, until tender, about 10 minutes, stirring occasionally. Remove the grill pan and vegetables from the grill and transfer the vegetables to a bowl. Brush the cut side of the buns with oil. Grill the patties over direct medium-high heat, with the lid closed, until cooked to medium doneness (160°F), 8 to 10 minutes, turning once. During the last 30 seconds to 1 minute of grilling time, place a slice of cheese on top of each patty to melt, and toast the buns, cut side down, over direct heat. Build each cheeseburger on a bun with a patty and onions and peppers. Serve warm.