Pour at least 2 inches of oil into a deep fryer or cast-iron skillet and heat it to 375°F. Watch the thermometer before adding batter so the oil is fully heated and ready to crisp the first strands.

Whisk the room-temperature eggs and milk in a bowl until the mixture looks light and lightly foamy, then combine the flour, sugar, sea salt, and baking powder in a separate bowl. The dry mixture should look evenly blended, with no concentrated pockets of baking powder.

Add the dry mixture to the egg mixture and whisk until the batter is completely smooth. Stop once the batter flows in a thick, steady ribbon, since excessive mixing can make the fried texture tough.

Transfer the batter to a pastry bag, funnel, or spouted measuring cup, blocking the funnel opening with a finger until you are over the oil. Hold the dispenser close to the surface so the batter can settle into neat loops instead of scattering.

Release the batter in an outer circle first, then fill the center with overlapping loops and crosswise strands; flip once the cake floats and turns honey golden. Fry the second side for about 45 to 60 seconds, until the lattice is golden on both sides and the sizzling has steadied.

Move the finished cake to the prepared wire rack and dust it with powdered sugar while hot. The elevated rack lets excess oil drain while keeping steam from softening the crisp edges.