In a pan over medium heat saute the corn kernels, carrots, snow peas, and peas in the butter and oil for a few minutes. Set aside.
In a pot boil the kalabasa cubes in just enough salted water until fork tender or until all water evaporates. Continue stirring for a few minutes to dry off kalabasa pieces. Turn off heat and mash finely. Mix in melted butter, salt, and ground black pepper until well combined. Mix in warm cream until well combined. Set aside.
In a bowl, mix together Chicken Mixture until well combined. Chill/freeze until solid. Cut into nuggets and coat with flour, egg, and breadcrumbs. Return to chiller/freezer until ready to fry. In a deep pot over medium heat, deep-fry chicken for about five minutes. Increase heat and double fry chicken until golden and crispy.
In a pan, saute onions and garlic in number until softened. Mix in flour and cook for about a minute. Whisk in broth until smooth. Add soy sauce, oregano, and bring to a boil. Season with salt and pepper according to taste.
Place a layer of the mashed kalabasa into the bottom of a container as a base. Place pieces of nuggets all over the top of the mashed kalabasa and sprinkle the cooked veggies on top. Top with a sprinkle of both kinds of cheese and a drizzle of gravy.