Begin by bringing a large pot of salted water to a boil. Add the jumbo shell pasta and cook according to package instructions until al dente. Once cooked, drain the pasta and set aside, allowing it to cool slightly.
In a large skillet, heat the olive oil over medium heat. Add the cubed chicken breasts and cook until they are no longer pink in the center, about 5-7 minutes. Stir occasionally to ensure even cooking. Season with salt and pepper to taste.
Once the chicken is cooked, add the chopped broccoli florets to the skillet. Sauté for an additional 3-4 minutes, or until the broccoli is bright green and tender. Stir in the curry powder for a unique twist on the flavor profile.
In a mixing bowl, combine the cream of chicken soup, milk, and melted butter. Mix until well combined. Add this creamy mixture to the skillet with the chicken and broccoli, stirring to combine all the ingredients thoroughly. Reserve ½ cup of shredded cheddar cheese for topping.
Preheat your oven to 350°F (175°C). Take a spoonful of the chicken and broccoli mixture and carefully stuff each jumbo shell. Place the stuffed shells in a greased baking dish, opening side up.
Once all the shells are stuffed, pour any remaining creamy mixture over the shells. Sprinkle the reserved cheddar cheese on top. Cover the baking dish with aluminum foil and bake for 25 minutes. Remove the foil and bake for an additional 10-15 minutes, or until the cheese is bubbly and golden.