Preheat oven to 350 F. Grease and line bottom and sides of an 8-inch square pan with parchment paper.
For crust, pulse walnut crumbs or pieces, sugar, flour, cloves and salt in a food processor until walnuts are finely ground. Add ground almonds and hazelnuts and pulse to blend. Cut butter into small pieces and add to nut mixture, pulsing until dough comes together (it will be soft). Scrape dough into prepared pan and press to flatten in bottom of pan (dip your hands in cold water to help prevent the dough from sticking). Bake for 18 to 20 minutes, until crust browns lightly. Allow to cool.
For filling, grind walnuts with brown sugar until fine. Whisk nut mixture with eggs, egg yolk, vanilla and baking powder until smooth. In a separate bowl, toss coconut, flour, cinnamon and cloves to coat. Add to brown sugar mixture and stir to blend. Pour into cooled tart shell and bake for 40 minutes, until top is richly browned and set. While warm, brush top of tarte with apricot or orange liqueur. Allow to cool at least 30 minutes before slicing.
Cake can be served warm or at room temperature, but store refrigerated until ready to serve.
Stir sugar and water together in a saucepot. With a paring knife or peeler, peel the oranges (orange part only, not the whites) and place the zest in the pot. Add cloves, cinnamon and nutmeg to the pot and bring up to a simmer. Simmer for just 3 minutes, then remove from heat and cool to room temperature. Strain out peel and spices and chill completely.
Juice the 4 oranges and strain out seeds and pulp. Stir juice into sugar syrup. Pour mixture into an ice cream maker and churn following manufacturer’s instructions. Once sorbet has churned for 10 minutes, whisk egg white in a small bowl until foamy, then pour into ice cream maker. Churn another 10 to 15 minutes, then spoon sorbet into a container and freeze until firm.