Preheat oven to 350°F (180°C). Lightly butter a deep 8-inch square or 9-inch round baking dish. Place the empty dish inside a larger roasting pan. Separate the eggs, placing the whites in a clean, medium bowl and the yolks in a large bowl. Zest and juice the lemons.

In the large bowl with the egg yolks, add the softened butter and sugar. Beat with a hand mixer on medium speed for 2-3 minutes until pale, fluffy, and smooth.

Beat the lemon zest and juice into the butter mixture. The mixture may look slightly curdled; this is normal.

Whisk the flour and salt into the wet ingredients until just combined. Then, gently stir in the milk until you have a thin, liquid batter. Set aside.

Using clean beaters, whip the egg whites on medium-high speed until they form soft, glossy peaks. The tips should curl over when the beaters are lifted.

Vigorously stir about one-third of the whipped egg whites into the lemon batter to lighten it.

Gently fold the remaining egg whites into the batter using a rubber spatula. Fold by cutting down through the center, sweeping along the bottom, and turning the mixture over itself. Rotate the bowl as you go until just combined, with minimal streaks of white.

Pour the batter into the prepared baking dish. Pull out the oven rack and place the roasting pan (with the dish inside) on it. Carefully pour hot water into the roasting pan until it comes about halfway up the sides of the pudding dish.

Bake for 40-50 minutes, until the top is golden brown, set to the touch, and the center has a soft, creamy jiggle.

Remove the pudding dish from the water bath. Let it cool for 10-15 minutes. Serve warm or at room temperature, dusted with icing sugar and optionally with whipped cream or vanilla ice cream.