1. Bring a medium saucepan of water to a boil. With a vegetable peeler, remove the zest from the oranges in long strips. Boil the strips in the water for 1 minute, then drain. Repeat this blanching 4 more times with fresh water to remove any bitterness. Transfer the zest to a food processor and finely chop. Remove the bitter white pith from the oranges, then chop the flesh into 1/2-inch pieces.
2. In a medium saucepan, combine the sugar, water, orange juice and lemon juice with the cinnamon stick, cloves, bay leaf and star anise and bring to a boil. Add the minced orange zest and simmer over low heat for 10 minutes. Add the chopped orange flesh and simmer until very thick, about 25 minutes.
3. Discard the spices and the bay leaf and transfer the mixture to a food processor. Process until thick and jamlike. Transfer the spoon fruit to a bowl and refrigerate until chilled, about 1 hour.
4. In a medium skillet, heat the olive oil. Add the almonds and cook over moderate heat until richly browned, about 3 minutes. Stir in the cardamom and season the almonds with salt and pepper. Let them cool completely.
5. Spread the spoon fruit on the toasted brioche and top with the feta. Sprinkle with the almonds and thyme and serve.