Trim the cheese into 12 even sticks about 4 inches long and 3/4 inch thick. Pat dry with paper towels to remove excess moisture so the coating adheres better.

Set up dredging stations

Place the flour in a shallow bowl and season with 1/2 tsp of the salt and the 1/8 tsp black pepper. In a second shallow bowl, whisk the 2 eggs with 2 tablespoons cold water until smooth. In a third shallow bowl, combine the breadcrumbs with the remaining 1/2 tsp salt and remaining 1/8 tsp pepper.

Coat the cheese

Working with one stick at a time, dredge a cheese stick in flour, shaking off excess. Dip into the egg wash, letting excess drip back into the bowl, then press into the breadcrumbs to coat completely. For a sturdier coating that prevents leakage, repeat the egg and breadcrumb step once more (egg → breadcrumbs a second time). Place coated sticks on a wire rack or baking sheet lined with parchment. Chill the coated sticks in the fridge for at least 20 minutes (or up to 1 hour) to firm up the coating — this reduces cheese leakage during frying.

Fry the tequeños

Pour the vegetable oil into a heavy-bottomed skillet or pot to a depth of about 1 to 1 1/2 inches (roughly 3–4 cups depending on pan). Heat oil over medium heat until it reaches 350°F (175°C) — if you don't have a thermometer, test with a small breadcrumb: it should sizzle and brown in about 30–40 seconds.

Fry the chilled tequeños in batches of 3–4 so they have room and oil temperature stays consistent. Fry each batch for 1.5–2.5 minutes, turning gently so all sides brown evenly, until golden brown. Avoid overcrowding the pan.

Use a slotted spoon or spider to transfer fried tequeños to a plate lined with paper towels to drain. Let rest 1–2 minutes; cheese will be hot inside.

Serve

Arrange six tequeños per serving on a platter. Serve immediately with guasacaca, chimichurri, ketchup or lime wedges as desired. For best texture, eat right away while hot and melty.