Beat the eggs with the sugar to pale yellow ribbons. Beat in the milk, oil and orange zest. In a small bowl, sift the flour with the baking powder, baking soda, and salt. Add the flour mixture to the egg mixture a tablespoon at a time, stirring well after each addition.
Pour batter into prepared cake pan and bake for 45 to 55 minutes or until middle of cake springs back when lightly touched. Remove cake from oven, let cool slightly on a rack, then invert and cool completely.
Meanwhile, prepare the syrup: Use a sharp paring knife to cut the orange rind off the orange used for zest and the remaining orange, leaving the bitter white pith on the orange. Cut the skin into very thin strips and reserve. Cut away and discard the white pith, remove the orange supremes, and reserve.
In a large saucepan, combine the orange juice, sugar, and thin orange strips. Bring to a simmer and cook for 30 minutes, or until a thick syrup. Strain the syrup and reserve the orange strips, along with 1/2 cup of the syrup. Use a toothpick to poke holes in the top of the cake, then pour the warm strained syrup all over the cake so that it soaks through.
Place the remaining 1/2 cup syrup in a small saucepan, bring to a simmer and reduce to a few tablespoons. Use a spatula to spread the thick glaze over the top of the cake. Place cake on a serving platter, and arrange the reserved orange strips and orange supremes on top of the cake.
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