Boil the pasta according to the package directions. Drain well and set aside. You should have approximately 3½ cups of cooked pasta.
Heat the oil in a large skillet over medium heat. Add the chopped broccolini and garlic. Sauté for about 2 minutes, stirring occasionally.
Peel and chop the carrots, then add them to the skillet. Lower the heat a bit. Cover and cook for approximately 4 minutes, or until the carrots begin to become tender.
Drain and rinse the chickpeas.
Uncover the skillet and add the smoked paprika, oregano, red pepper flakes, and chickpeas.
Pour in the coconut milk and cook for another 1 to 2 minutes, stirring so the spices and coconut milk coat the vegetables. Remove the skillet from the heat.
Rinse and chop the celery, red onion, and red bell peppers. Thaw out the peas by placing them in a bowl. Then, add all these to a large bowl. Add the sautéed veggies and cooked pasta to the fresh veggies.
Gently toss everything together until the pasta and vegetables are evenly coated.
Season with salt and black pepper to taste. If you have some parsley around, garnish this with some parsley.
Serve warm, at room temperature, or chilled.