Adjust oven rack to lower-middle position and heat oven to 325 degrees. Pat pork dry with paper towels and season with salt and pepper. Heat 1 tbsp oil in Dutch oven over medium-high heat until just smoking. Brown half of pork on all sides, about 8 minutes; transfer to bowl. Repeat with 1 tbsp oil and remaining pork; transfer to bowl.
Add remaining 1 tbsp oil, leeks, ½ tsp salt, and ½ tsp pepper to fat left in pot and cook over medium heat, stirring occasionally, until softened and lightly browned, 5 to 7 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Stir in tomatoes and their juice, scraping up any browned bits, and cook until tomato liquid is nearly evaporated, 10 to 12 minutes.
Stir in wine, broth, bay leaf, and pork with any accumulated juices and bring to simmer. Cover, transfer pot to oven, and cook until pork is tender and falls apart when prodded with fork, 1 to 1 ½ hours. Discard bay leaf. Stir in oregano and season with salt and pepper to taste. Serve.