Soak the beans overnight (8-12 hours). Place dried gigantes in a large bowl, cover with at least 3 inches of cold water. After soaking, drain and rinse.
Pre-boil the beans. Cover soaked beans with fresh cold water. Bring to a boil, skim any foam. Simmer 35-45 minutes until 70% cooked - tender outside but still firm at center. Drain and set aside.
Preheat oven to 375F (190C).
Build the tomato sauce. Heat 4 tablespoons olive oil over medium heat. Saute onion, celery, and carrot 7-8 minutes. Add garlic and cook 1 more minute. Add tomatoes, tomato paste, paprika, oregano, bay leaf, sugar, salt, pepper, and water. Simmer 10 minutes until slightly thickened.
Combine and bake. Transfer sauce and pre-cooked beans to a large baking dish. Stir gently. Drizzle remaining 2 tablespoons olive oil over top. Bake uncovered at 375F for 45-55 minutes until sauce is thick, edges are caramelized, and beans are fully creamy.
Rest 10-15 minutes before serving. Scatter fresh parsley over top and squeeze lemon at table. Serve with thick slices of country bread.