Preheat your oven to 400°F.
In a large skillet, heat 1 tablespoon of olive oil over medium heat. Once hot, add the chicken cubes and cook until browned, about five minutes. Remove from the skillet using a slotted spoon and set aside.
Next, bring four cups of water to a boil in a large pan. Add the jumbo shells, and cook them to al dente, about ten minutes. Strain and set aside.
In a small saucepan, combine 2 cups of cream of chicken soup, ½ cup of milk, 2 tablespoons of unsalted butter, and 1 teaspoon of curry powder. Stir over low heat for ten minutes until warmed through.
Cover the bottom of a 9×13-inch casserole dish with a thin layer of sauce.
In a large bowl, mix the cooked chicken, broccoli, and 1 cup of cheddar cheese. Fill each shell with the mixture and place in the dish.
Pour the remaining sauce over the filled shells and sprinkle the rest of the cheese on top.
Bake in the preheated oven for about twenty minutes until the cheese is melted and bubbly.
Remove from the oven and let cool for a few minutes before serving.