Beat the yolks with the whip attachment on high speed until they are thick and lemon-colored, 3 to 5 minutes.
While beating on medium speed, gradually add 1/2 cup of the sugar.
Scrape the bowl, and beat on high speed about 5 minutes more, until the yolks are very thick and almost white in color and form a slowly dissolving ribbon as they fall off the beaters (NOTE: If your yolks are very yellow or orange, they will just turn a lighter shade of yellow, not white, after beating).
Beat in the vanilla and lemon zest.
Scrape the yolks into a large wide bowl.
Wash and dry the bowl and beaters.
In the clean bowl with clean beaters, whip the whites with the salt on medium speed until the whites have thickened to the point where the beaters leave traces in the whites.
Gradually add the remaining 1/4 cup sugar and continue beating on medium speed until the whites form stiff, shiny peaks that curl slightly at their tips. The whites should have a creamy, moist texture.
Sprinkle about 1/4 of the nuts and bread crumbs over the yolks (you’ll see the nuts and crumbs look and feel moist) and add about 1/4 of the whites.
Fold everything together very gently, with just a few broad strokes of the spatula, to deflate the batter as little as possible. It’s all right if streaks of white remain at this point.
Repeat with 3 additions of the remaining nuts and whites, folding in the last addition just until no whites show. The batter should look light and airy.
Divide the batter evenly among the prepared pans (a kitchen scale is helpful for this step) and rotate each pan gently on the countertop to level the batter.
Place the pans in the oven, two on the upper rack, and one on the lower rack.
Bake for 20 to 25 minutes, until the layers are golden brown, they spring back when gently pressed, and a toothpick comes out clean. Be careful not to overbake. Begin testing for doneness at the earlier time; the bottom layer may be baked a minute or two before the other layers.
Cool the cakes in their pans for 10 minutes. The cakes will settle on cooling and will be about 1 inch tall.
Release the layers from the sides of the pan by running the tip of a sharp knife all around the edges of the cakes.
Cover the cakes with wire racks and invert.
Carefully lift off the pans and peel off the papers.
Cover the layers with other racks and invert again to cool right side up.
Cakes may be made to this point a day ahead; when completely cool, wrap layers in plastic wrap and leave them at room temperature overnight.