Preheat oven to 375 degrees. Heat a very large ovenproof skillet with a lid over medium high. Add oil and swirl to coat pan. Add leeks in as close to a single layer as possible. Cook until beginning to brown, 4 to 5 minutes. Add orange juice and stock and season with 1 1/4 teaspoons of salt. Turn leeks over and place oranges and thyme on top. Bring liquid to a boil.
Cover and place in oven until leeks are tender, about 30 minutes. Remove from oven and turn oranges over, spooning some liquid over the top. Return to oven, uncovered, and cook until oranges and leeks are browning and liquid is syrupy, spooning liquid over the top twice, about 30 minutes more. If necessary, remove from oven and boil over high heat until liquid reaches desired consistency, about 1 minute more.