Start by mixing the filling. In a large bowl, combine the shredded chicken and softened cream cheese. Make sure your cream cheese is truly at room temperature – this makes a huge difference in getting everything to mix evenly. Use a wooden spoon or rubber spatula to really work them together until well combined.
Add the shredded Mexican cheese blend, green chilies (don’t drain them – the moisture helps), chili powder, garlic powder, cumin, salt, and pepper. Mix until everything is evenly distributed. Give it a taste and adjust the seasonings if needed – the filling should be pretty flavorful since it’ll be wrapped in plain tortillas.
Heat about 3-4 inches of vegetable oil in a heavy-bottomed pot or deep skillet over medium heat. You’re aiming for around 350°F – if you drop a small piece of tortilla in, it should bubble actively but not violently.
While your oil heats, warm your corn tortillas. This is crucial – cold tortillas will crack when you roll them. Working in batches of 4-5, wrap them in slightly damp paper towels and microwave for 30-40 seconds until they’re pliable and steamy.
Working with one warm tortilla at a time, place about 2-3 tablespoons of filling in a line across the lower third of the tortilla. Roll it up tightly, making sure the filling stays tucked in. Place seam-side down on a plate and repeat with remaining tortillas. Keep your rolled taquitos covered with a clean kitchen towel to prevent them from drying out.
Once your oil is hot, carefully place 3-4 taquitos seam-side down in the oil. They should sizzle immediately but not too aggressively. Fry for about 2-3 minutes until golden brown on the bottom, then use tongs to carefully flip them. Cook another 1-2 minutes until they’re evenly golden brown all over.
Remove to a paper towel-lined plate, standing them on their sides if possible to keep them crispy. They should be a deep golden color and make a hollow sound when tapped lightly.
Let them cool for a few minutes before serving – the filling will be extremely hot. Serve while still warm and crispy, when the cheese is still melty and the outside has a satisfying crunch.