Heat the vegetable oil in a large pan over low heat. Add the finely chopped onions and garlic. Sauté for about 10 minutes, stirring occasionally, until softened. Season with salt and pepper.
Stir in the Peruvian Aji Amarillo paste and continue to cook over low heat for an additional 8 minutes, until fragrant.
While the onions and garlic are cooking, blend the evaporated milk and ciabatta bread together until smooth.
Add this mixture to the pan with the onions and garlic. Cook over medium heat, gradually adding the vegetable broth. Stir continuously for about 4 minutes, until the sauce has thickened and become creamy.
Add the cleaned and peeled crawfish to the pan. Cook for 3 minutes, or until the crawfish are cooked through. Taste the sauce and adjust the seasoning with additional salt and pepper if needed.
Boil or steam the peas and diced carrots until tender.
Add the boiled and diced potatoes, peas, and carrots to the sauce. Stir to combine and heat through.
Garnish with Parmesan cheese, if desired, before serving.