Heat the oven to 350F. Spread the almonds on a sheet pan and toast for 8 to 10 minutes, until they smell nutty and the skins have darkened a shade. Cool them completely, then chop half of them coarse and leave the rest whole. Line two sheet pans with parchment.

Whisk the melted butter with the sugar until it looks like wet sand, then whisk in the eggs, the extra yolk, the lemon zest and both extracts. The butter must be lukewarm rather than hot or it will scramble the yolks.

Stir the flour, baking powder, salt and nutmeg together, add them to the bowl and mix with a wooden spoon until a stiff, slightly sticky dough forms. Fold in the whole and chopped almonds. Do not use a mixer, which whips air into a dough that should stay dense.

Divide the dough in two and shape each half on a lined sheet into a log about 11-inch long and 2 1/2-inch wide, then flatten the tops to roughly 3/4-inch with damp hands. Leave plenty of room between them because they spread. Brush with the egg white beaten with the water and scatter over the turbinado sugar.

Bake at 350F for 28 to 32 minutes, until the logs are firm, golden and cracked along the top. A skewer into the middle should come out with a few moist crumbs rather than wet dough.

Cool on the sheet for exactly 20 minutes, then slide each log onto a board. This rest is the single most important step: at 20 minutes the log is warm to the hand and cuts cleanly, while a hot log tears and a cold one shatters.

Turn the oven down to 325F. Using a long serrated knife and long sawing strokes with almost no downward pressure, cut each log on a slight diagonal into slices a generous 1/2-inch thick. Lay them cut-side down on the sheets.

Bake for 12 minutes, turn every slice over, and bake for a further 12 minutes. They should be pale gold, firm, and sound hollow when tapped. Cool completely on a rack, where they finish crisping, then store airtight at room temperature.