Preheat the oven to 350°F.

Choose a heavy-bottomed ovenproof skillet or Dutch oven that’s large enough for the flank steak to lie flat but is as snug as possible. Add 2 tablespoons of the oil to the skillet over high heat. Once the oil starts to smoke, add the meat and cook for 5 to 7 minutes on each side, until deep brown in color. Remove the meat from the skillet and set the meat aside.

Add the carrot and onion to the skillet, followed by the garlic. Sauté the vegetables over medium-high heat until they start to brown but are still firm. Return the meat to the pan. Add the red wine – enough to come three-fourths of the way up the side of the meat. Add the thyme and 1 teaspoon of the salt, cover the skillet, and transfer to the oven. Braise the meat for about 2 ½ hours, until the meat can be pulled apart with a fork. Transfer the meat to a plate to rest and cool.

Reserve and strain the pan juices and pour into a saucepan. Over medium-low heat, reduce the juices until thickened. With two forks, separate the meat into chunky strings and roughly cut them crosswise into 2- to 3-inch pieces. Place the meat in the pot with the reduced juices and coat well.

Preheat the panini grill to high heat.

Brush the red onion with the remaining 1 tablespoon vegetable oil. Grill the onions for about 2 minutes until charred on the outside and slightly cooked on the inside. Place in a bowl and separate into rings. Add the peppers, olive oil, sherry vinegar and remaining 1 teaspoon salt and mix well.

Reduce the panini grill heat to medium-high.

For each sandwich: Slice a ciabatta roll in half. Place 1 slice of cheese on the bottom half. Add the meat, the onions and peppers and another slice of cheese. Close the sandwich with the top half of the roll. Grill the sandwich for 3 to 4 minutes until the cheese is melted.