Preheat the oven to 180 C / Gas 4. Butter and flour two cake tins. For cake: Sift together the flour, baking powder and salt. Whisk together the buttermilk and egg whites in a medium bowl.
Put the 340g sugar and lemon zest in a mixer bowl or another large bowl and rub them together with your fingers until the sugar is moist and fragrant.
Add the butter and working with the paddle or whisk attachment, or with a hand mixer, beat at medium speed for a full 3 minutes, until the butter and sugar are very light. Beat in the extract, then add one third of the flour mixture, still beating on medium speed.
Beat in half of the milk-egg mixture, then beat in half of the remaining dry ingredients until incorporated. Add the rest of the milk and eggs beating until the batter is homogeneous, then add the last of the dry ingredients. Finally, give the batter a good 2-minute beating to ensure that it is thoroughly mixed and well aerated. Divide the batter between the two tins and smooth the tops with a rubber spatula.
Bake until the cakes are well risen and springy to the touch – a thin knife inserted into the centers should come out clean, 30 to 35 minutes.
Transfer the cakes to cooling racks and cool for about 5 minutes, then run a knife around the sides of the cakes, unmould them and peel off the paper liners. Invert and cool to room temperature, right side up (the cooled cake layers can be wrapped airtight and stored at room temperature overnight or frozen for up to two months).
For Filling: Combine the 170g sugar, cornflour and 1/8 teaspoon salt in a small saucepan. Gradually add water and whisk until well blended. Whisk in 2 egg yolks (save the remaining 2 egg yolks for another use), lemon peel and lemon juice. Cook over medium heat, whisking constantly until thick and bubbly. Boil one minute; remove from heat. Stir in butter. Cool to room temperature, without stirring.
When the cake and filling are made, put one cake on the plate, and put some of the lemon filling on it, then put the other/second half of the cake on top.