In a large cast-iron Dutch oven, heat the oil over high heat until it reaches 375 degrees F on a deep-fry thermometer.
To make the batter, in a large bowl, whisk together the cornmeal, baking powder, cayenne pepper and 1 teaspoon salt. In a second bowl or large liquid measuring cup, combine the beer, eggs and onions. Add some salt and pepper and whisk until smooth. Stir the wet ingredients into the dry ingredients, using as few strokes as possible. (The mixture should resemble wet sand; add more beer, if needed.)
Line a plate with paper towels and set by the cooktop. To fry the hushpuppies, scoop up the batter using a medium ice cream scoop and drop it into the hot oil without crowding. Fry, stirring occasionally with a slotted spoon, until golden brown, 3 to 5 minutes. Remove with a slotted spoon to the prepared plate. Adjust the heat to maintain the proper temperature and repeat with the remaining batter. Serve immediately.