Chill the cheese curds in the refrigerator until very cold, 15–20 minutes; this helps them hold their shape when fried.
Pour the vegetable oil into a deep, heavy pot to a depth of 2–3 inches and heat to 360–370°F over medium-high heat. Set a wire rack over a baking sheet for draining.
In a shallow bowl, toss the cold cheese curds with 0.5 cup all-purpose flour to lightly coat; shake off excess.
In a medium bowl, whisk together 1 cup all-purpose flour, cornstarch, baking powder, kosher salt, and black pepper.
Whisk in the cold lager beer until a smooth, medium-thick batter forms that clings to a spoon; if very thick, add a splash more beer. Let stand 5 minutes while the oil stabilizes at temperature.
Working in batches, dip floured curds into the batter, letting excess drip back, and carefully lower into the hot oil. Fry until golden and crisp and the curds float, 1.5–2.5 minutes, adjusting heat to maintain 360–370°F.
Remove with a spider or slotted spoon and drain on the rack. Immediately sprinkle each batch with the fine salt.
Serve hot with ranch dressing or marinara sauce (for serving).