Slice the queso de freír into 12 equal pieces, about 2 x 3 inches and 1/4 inch thick; pat each slice dry with paper towels to reduce splattering.
Pour the oil into a medium pan to a depth of about 1/4–1/2 inch and heat over medium-high until it reaches roughly 350°F (175°C) or is shimmering.
Test-fry one slice first: carefully add a single slice and fry until the bottom is golden brown, about 1–2 minutes; if it melts instead of browning, remove it and dust the remaining slices lightly with corn starch, shaking off excess.
Fry the slices in batches without crowding so the oil stays hot; cook each side until golden brown, about 1–2 minutes per side, flipping once with tongs or a spatula.
Transfer fried cheese to a plate lined with paper towels to drain briefly, then serve immediately while hot and crisp.