After you peel and clean the shrimp, transfer the shells to a sauce pan and cover with 2 cups of water. Bring to a boil, reduce heat and cook for 5 minutes. Remove from heat and set aside.
In a large dutch oven pot, add the butter and olive oil. Heat to medium, add the onion, garlic and carrots. Season lightly with salt and pepper and cook for 6 to 8 minutes. Add the aji paste and cook for 2 more minutes
Add the tomatoes, oregano, cumin and bay leaves. Add another pinch of salt and pepper and cook for 5 minutes. Add the chicken broth, vinegar and strain shrimp stock directly into soup. Bring to a boil, reduce to a simmer and taste for salt.
Add the potatoes and bring back up to a simmer. Cook for 10 minutes. To the beaten eggs,slowly stream in about 1/3 cup of hot broth from soup, whisking the whole time. Add egg mixture to the soup and stir to combine. Add in the cabbage, peas and room temperature milk. When soup comes back up to a simmer, add in the shrimp and cook for 5 more minutes. Remove from heat, cover and let sit for 5 more minutes. Garnish with queso fresco and cilantro. Yields 6-8 servings.