Step 1

Make the basbousa: Place a rack in the center of the oven and preheat to 350° F. Grease an 8- by 8-inch square cake pan and line the bottom and two sides with a sheet of parchment paper, leaving 3 inches of overhang on two of the sides.

Step 2

In a medium bowl, whisk together the semolina, baking powder, cinnamon, salt, and nutmeg. In a large bowl, whisk together the melted butter, sugar, and vanilla. Beat in the eggs, one at a time, then continue whipping until the batter is frothy, about 2 minutes. Gently fold the dry ingredients into the butter mixture just until no dry streaks remain, then fold in the pumpkin purée. Pour the batter into the prepared pan, smooth the surface, and bake until a toothpick inserted into the middle comes out clean, 25–30 minutes. Set aside to cool to room temperature.

Step 3

Meanwhile, make the chai syrup: In a small pot, stir together the sugar and 1½ cups water over low heat until the sugar has completely dissolved, about 2 minutes. Add the teabags, cardamom, cinnamon stick, and cloves, bring it to a boil, then turn the heat down to maintain a strong simmer. Cook until the syrup is concentrated and deeply flavorful, about 10 minutes. Turn off the heat, remove and discard the spices, then transfer the teabags to a small sieve. Hold the sieve above the saucepan, pressing on the teabags to extract as much liquid as possible, then discard them. Stir in the butter and orange juice, then set the syrup aside to cool to room temperature.

Step 4

When the cake has cooled, poke it all over with a toothpick, around 12 times. Pour the cooled syrup over the cake, cover loosely with foil, and set aside for 1 hour to allow the cake to absorb the liquid. Slice the basbousa into 12 pieces and serve warm or at room temperature. Basbousa keeps well in an airtight container for up to 3 days.