1. Heat the oven to 350°F (175°C). Butter and flour a 9-by-13-inch (23-by-33 cm) shallow baking pan; set aside.
2. In a large bowl, beat the egg yolks with a whisk or hand mixer until thick and pale lemon-colored, 3-4 minutes. Gradually add half the sugar (1/2 cup / 100 g), beating continuously until the mixture is light and slightly ribboning.
3. Add the hot water (approximately 160-180°F / 70-82°C) to the yolk mixture and stir to combine, then mix in the remaining sugar (1/2 cup / 100 g) and the lemon extract.
4. In a separate clean bowl, beat the egg whites until stiff peaks form — the whites should hold a firm, glossy peak and not slide when the bowl is tilted.
5. In a small bowl, whisk together the flour, baking powder, and salt. Sift this dry mixture over the yolk-water mixture and fold gently until just combined — do not overmix.
6. Fold the stiff egg whites into the batter in two additions, using a wide spatula and a gentle under-and-over motion, until no white streaks remain.
7. Pour the batter into the prepared pan and bake at 350°F (175°C) for 23-27 minutes, until the top is golden and springs back when lightly pressed in the center, and a wooden skewer inserted in the middle comes out clean.
8. Remove from the oven and allow the cake to cool in the pan on a wire rack for 10 minutes before turning out.
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