Grease a half sheet pan and line with parchment paper or a nonstick rubber mat (if using a nonstick rubber mat, grease only the frame of the sheet pan).
Sift the flour, baking powder, and salt together twice.
Warm the eggs to 27°C / 80°F over a hot water bath, whisking constantly. Reserve warm.
Combine the walnut paste, butter, and sugar in a 12-qt mixer bowl fitted with the paddle attachment and mix on medium speed until creamed, about 7 minutes. Scrape down the sides of the bowl often.
Slowly pour in the warm eggs in 4 additions to ensure a proper emulsion. Scrape down the sides of the bowl after each addition of eggs.
Turn the mixer off. Add the dry ingredients all at once and mix on low speed until just combined. Scrape the sides of the bowl as well the bottom and mix on low speed for a few more seconds.
Spread the batter evenly in the prepared sheet pan.
Bake until the batter is cooked through, golden brown, and springs back when pressure is applied, about 15 minutes. Always test the center of the pan, where it will take the longest to bake. Let cool to room temperature.
Before cutting the cake, freeze it for 45 minutes to 1 hour. It cuts very cleanly when it is partially frozen.
Cut the cake into rectangles 2.5cm / 1in by 5cm / 2in by 2.5cm / 1 in.
Reserve in an airtight container at room temperature. Discard after service.