In a small bowl, mash the chopped garlic into a rough paste.
Add the vegetable oil to a saucepan over medium heat. Heat the oil, then add the onion, aji amarillo pepper, and garlic. Sauté the mix, stirring often, until the onions are translucent and soft (approximately 7 to 8 minutes).
Pour the pepper, onion, and garlic mix into a blender (or a large bowl if using a handheld food processor). Add the evaporated milk, and blend the sauce until smooth. Crumble the crackers into the sauce and add the queso fresco, salt, and black pepper. Blend again to smooth (yet still relatively thick).
Add additional salt and pepper to taste.