Slice the onions crosswise about 1/2-inch thick and then carefully separate the slices into rings. (You should have about 8 cups.) Place the rings in a wide, shallow dish in as few layers as possible.

In a bowl, whisk together the milk and ice water. Pour evenly over the onions. Cover the dish with plastic wrap and refrigerate for at least 2 hours or as long as overnight. Very carefully turn the rings at least once to soak them evenly.

Make the batter. In a large bowl, whisk together the flour, salt, dry mustard and pepper; set aside. In a bowl, lightly beat the eggs; whisk in the vegetable oil, and then the beer and Tabasco, mixing well.

Make a well in the center of the flour mixture and pour in the egg mixture all at once. Using a whisk and starting in the center of the bowl and working outward, whisk until the mixture is free of lumps.

Cover and let stand for at least 2 hours or as long as overnight.

Line 2 baking sheets with a double layer of paper towels. Using tongs, remove the onion rings from the milk mixture, shaking off the excess liquid, and let drain on one of the prepared sheets. Pat the onion rings dry with more paper towels to remove all excess moisture.

In a deep-fat fryer or large, heavy saucepan over medium-high heat, pour in vegetable oil to a depth of at least 3 inches (7.5 cm). Heat until the oil registers 375°F  on a deepfat frying thermometer, or until a small cube of bread dropped into the oil browns in about 45 seconds.

Stir the batter. Working in batches and using the tongs, dip the onion rings into the batter, shaking off any excess; quickly but carefully drop them into the hot oil. Fry the onion rings, turning occasionally with the tongs, until a deep golden brown, 4-5 minutes.

Transfer the cooked onion rings to the other paper towel-lined baking sheet and let drain briefly.

Serve immediately.