Step 1In a small saucepan, combine the sugar, water and orange zest strips. Heat over low heat, stirring to dissolve the sugar. Stop stirring, raise the heat to medium-high and bring to a boil. Simmer uncovered over medium-low heat until thickened slightly, about 5 minutes. Add the orange and lemon juice and continue to simmer for 1 minute, then remove from the heat. Cool the syrup until warm, about 10 minutes, then remove the orange zest and discard. Set aside.
Step 1Heat the oven to 275 degrees. Toast the hazelnuts in a shallow baking pan until the nuts are fragrant and their skins are slightly darker (be careful not to overtoast), about 12 minutes; shake the pan about halfway through the roasting time. Wrap them in a clean kitchen towel and set aside for 5 minutes. Rub the hot hazelnuts vigorously with the towel to remove some of the skins, then place the nuts in a sieve and continue rubbing with the towel to remove the skins (not all of the skins may rub off; this is OK). Set aside to cool completely.
Step 2Increase the oven temperature to 350 degrees. Oil a 9-inch square cake pan. Line the base with waxed paper or foil; oil the paper or foil.
Step 3Grind the hazelnuts with the sugar in a food processor to a fine powder but not to a paste. Scrape down the sides once or twice. Transfer the mixture to the bowl of a stand mixer or to another large bowl.
Step 4Add one egg to the hazelnut mixture and beat over low speed until combined. Add the second and beat again at low speed, then increase the speed and continue beating until the batter is pale, thick and smooth, about 2 minutes. Repeat with the remaining eggs, until each is blended in thoroughly, scraping down the bowl occasionally. Stir in the orange and lemon zests.
Step 5Sift the potato starch with the salt over the batter and fold it in gently but thoroughly. Gently beat in the oil in a fine stream until it is completely blended into the batter.
Step 6Transfer the batter to the cake pan. Bake until the cake comes away slightly from the pan’s edges, and a cake tester inserted into the center of the cake comes out clean, about 20 minutes. Remove the cake and cool it on a rack for a few minutes.
Step 7To remove the cake from the pan, run a metal spatula around the edges of the cake, and carefully turn the cake out onto a rack. Remove the paper and cool the cake to room temperature.
Step 8Turn the cake over onto another rack and invert onto a serving plate, so that the bottom of the cake faces up. Make 20 to 30 holes in the cake with a cake tester, spacing them evenly.
Step 9Slowly and evenly ladle the syrup, a few tablespoons at a time, over the cake, making sure to moisten it all over. Let the cake stand for 1 hour before serving, occasionally dipping a brush in the extra syrup on the plate and dabbing it gently on the cake.
Step 10Cut the cake in diamond-shaped pieces or squares. Garnish the center of each piece with a generous pinch of minced pistachios and serve with the strawberries.