In a large mixing bowl, combine 2 cups of whole wheat flour, 1/2 teaspoon salt, and 1 tablespoon oil. Gradually add water and knead the dough until it becomes soft and pliable. Cover the dough and let it rest for 20 minutes.
In another bowl, mix 1 cup grated cauliflower, 1 cup grated cabbage, 1/2 cup grated carrot, 1/2 cup finely chopped onion, 1/2 cup boiled and mashed potatoes, 1/4 cup chopped coriander leaves, 1/2 teaspoon grated ginger, 1/2 teaspoon chopped green chilies, 1/2 teaspoon garam masala, 1/2 teaspoon red chili powder, 1/2 teaspoon cumin powder, and salt to taste. Mix well to form the filling.
Divide the dough into equal portions and roll each portion into a small ball. Flatten each ball and place a spoonful of the vegetable filling in the center. Bring the edges together and seal the dough, enclosing the filling.
Dust the filled dough ball with some dry flour and gently roll it out into a 6-7 inch circle, taking care not to let the filling spill out.
Heat a tawa or griddle over medium heat. Place the rolled paratha on the tawa and cook for 1-2 minutes on each side until golden brown spots appear. Apply a little ghee or oil on both sides and cook for another 30 seconds on each side.
Remove the paratha from the tawa and serve hot with yogurt, pickle, or your favorite curry.