Preheat the oven to 150ºC . Grease two 9x5 inch loaf pans and dust lightly with flour.
In a large bowl, beat the butter with an electric mixer until creamy. Gradually sift the powdered sugar into the butter, stirring occasionally to partially combine. When all the sugar has been added, beat until fluffy. Gradually add the eggs, beating well after each addition. Add the vanilla, flour, and nutmeg; mix well. Divide the batter between the two pans.
Bake on the bottom rack of oven for 45 minutes. Rotate the pans to the top rack and bake for 10 minutes longer or until a toothpick inserted into the centers of the cakes comes out clean.
Remove from the oven and cool in pans for 30 minutes.
Meanwhile, make the Lemon Basil-Orange Syrup: Place the orange juice, water, sugar, and basil in a deep-sided saucepan. Bring to a boil over high heat and cook for 15 minutes, stirring frequently to prevent the mixture from boiling over. When the mixture is thick and syrupy, remove from the heat and strain. Cool to room temperature. If the syrup becomes thicker than pouring consistency, thin with about 2 tablespoons of very hot water.
Using a long, thin, wooden skewer, poke each cake all over from the top to the bottom. Drizzle half of the syrup over each cake, taking care to spread the syrup evenly into the tiny holes. Let cakes stand at least 2 hours before serving or cover with foil and keep up to 1 week in the pan.
To serve, remove the room-temperature cakes from pans and cut into 3 cm slices. Garnish with sprigs of basil.
This recipe makes two cakes; if you can only use one at a time, freeze the second cake, wrapped tightly in plastic and then in foil. However, once the cakes are drizzled with the syrup they will keep at cool room temperature for up to one week.