Preheat oven to 350º F (180ºC).
Grease a 10 or 12-cup bundt cake pan (26cm) with 2 tablespoons shortening, covering every angle, nook and cranny. Dust with 2 tablespoons all-purpose flour, shaking off excess. Reserve.
Beat softened 1 ½ cups unsalted butter in a large bowl with an electric mixer, or in a stand mixer with the paddle attachment, slowly adding 3 cups sugar and beating for 2 to 3 minutes after all is added.
Add 5 eggs, one at a time, beating well after each addition.
Add 2 tablespoons orange zest, 3 tablespoon orange liqueur or orange juice, and 1 teaspoon vanilla extract.
Sift 3 cups all-purpose , 1 teaspoon baking soda and ¼ teaspoon salt together in a small bowl or have them measured and sift directly over the butter mixture, as I do.
Add the dry ingredients (also called the flour mixture) in three additions alternating with ¾ cup milk in two additions. Don't overbeat after adding flour, simply beat just until incorporated.
Transfer 1 cup of this mixture to a small bowl and mix into it the sifted ⅓ cup unsweetened cocoa powder. Gently mix until you have a smooth batter.
Add half the orange batter into the prepared pan, spreading evenly. Drop half of the cocoa mixture over it, and swirl a few times with the tip of a knife. Repeat with the remaining batters. You will have to layers of marbled cake mix.
Bake for 1 hour or until a cake tester or toothpick inserted in the center comes out clean. It might take several more minutes.
Transfer to a wire rack and let cool for about 20 minutes.
Remove from the bundt pan, it will still be quite still hot, so be careful. Place on the cooling rack and let cool completely before glazing.
Pour the chocolate glaze on top of the cake and let it drip down the sides. You can scoop the drippings and pour them over again. Do this quickly before it sets. You can decorate with orange slices, orange peel, or rind.m