Calf's Liver, Caramelized Onion, and Tomato Sandwiches (Fegato alla Macellara)

Ingredients

• 1 ¹⁄₄ lb. cleaned calf's liver, cut into 1-inch–wide, 1/4-inch–thick strips
• ¹⁄₄ cup plus 2 tbsp. olive oil
• Kosher salt and freshly ground black pepper
• 4 medium yellow onions, thinly sliced lengthwise
• 6 oz. cherry tomatoes, halved
• 2 tsp. finely chopped thyme
• 6 ciabatta sandwich loaves, split