1. Line a large baking sheet with parchment and place two 7 inch pastry rings on it, ungreased. Preheat the oven to 465°F, 240°C.

2. Grind the pistachios in a food processor until very fine but not oily. Do not over process.

3. Add the cake flour and powdered sugar to the ground pistachios. Pulse to combine. Set aside.

4. Whip room temperature egg whites with cream of tartar and salt until foamy. Gradually add the granulated sugar, 1 tablespoon at a time, whipping 30 to 60 seconds between additions until very stiff and glossy.

5. Gently fold in half of the pistachio mixture. When incorporated, fold in the remaining pistachio mixture, keeping as much air as possible.

6. Divide the batter between the rings and spread flat.

7. Place in the oven, then immediately reduce temperature to 350°F, 180°C. Bake 15 minutes.

8. Turn off the oven and crack the door slightly. Leave the dacquoise inside for 60 minutes. Move to the counter and cool completely in the rings.

9. Run a thin knife around the edges to release the two dacquoise layers.

10. For the buttercream, whip egg yolks on medium high until very pale.

11. Heat sugar and water in a small saucepan to 240°F, 115°C. With the mixer on low, stream the syrup into the yolks, avoiding the whisk and bowl sides.

12. Increase to high speed and whip until the bowl is no longer warm. This can take about 10 minutes.

13. Add softened butter a few small pieces at a time, whipping to incorporate between additions. If it looks thin, keep whipping until thick and glossy.

14. Beat in vanilla and pistachio paste. Add a pinch of salt to taste.

15. To assemble, place one dacquoise layer on a board. Pipe small dollops of pistachio buttercream over the top, or pipe a ring and spread some cream in the center.

16. Top with the second dacquoise. Pipe decorative dollops of buttercream over the top layer.

17. Garnish with chopped pistachios around the edge. Chill 20 to 30 minutes to set slices cleanly. Serve at cool room temperature.