Peel and dice the potatoes into small cubes to ensure even cooking.

Chop the onion finely and set aside.

In a small bowl, whisk together the eggs and milk, then season with salt and pepper.

Prepare the salsa by combining diced tomatoes, cilantro, jalapeño, lime juice, and salt in a bowl; mix well and refrigerate.

Heat 1 tablespoon of vegetable oil in a large skillet over medium heat and add the diced potatoes; cook for about 10 minutes until golden and tender, stirring occasionally.

Add the chopped onion and cook for 3 minutes more until translucent.

In a separate pan, cook the chorizo over medium heat, breaking it apart with a spoon, until fully cooked and browned, about 5 minutes; drain excess fat.

Push the potatoes and onions to one side of the skillet, then pour in the egg mixture on the other side; cook gently, stirring until scrambled and just set.

Combine the chorizo with the potatoes, onions, and eggs, then remove from heat.

Warm the flour tortillas in a dry skillet or microwave until soft and pliable.

Divide the chorizo, potato, and egg mixture evenly among the tortillas, sprinkle with shredded cheddar cheese, and add a spoonful of salsa.

Roll up each tortilla tightly into a burrito, folding in the sides to secure the filling, then serve immediately.