Heat the oil in a pot over medium heat. Add the onion and sauté until it softens.
Add the carrot and stir it with the onion for a little while.
Add the corn, red bell pepper, and peas. Stir all the vegetables for a few minutes.
Add the tomato paste, then season with red pepper flakes, black pepper, and salt.
Pour the water over the ingredients and let the pot simmer over low heat for about 15-20 minutes.
Add the pasta and let it cook with the vegetable mixture for an additional 15 minutes until fully cooked.
Pour the vegetable pasta into a serving dish and serve hot.