Step 1: Preheat your oven to 325°F (160°C). Grease and flour a 10-inch Bundt pan or a 12-cup tube pan, ensuring all crevices are well-coated.
Step 2: In a large mixing bowl, cream together the 3 cups of white sugar, 1 cup softened unsalted butter, and ½ cup shortening with an electric mixer until light and fluffy (this usually takes about 5-7 minutes).
Step 3: Add the 6 large eggs, one at a time, beating well after each addition until fully incorporated. Scrape down the sides of the bowl as needed.
Step 4: In a separate bowl, whisk together the 3 cups sifted cake flour, ½ teaspoon baking powder, and ⅛ teaspoon salt.
Step 5: Gradually add the dry ingredients to the wet ingredients, alternating with the 1 cup heavy cream. Begin and end with the dry ingredients. Mix on low speed until just combined, being careful not to overmix.
Step 6: Stir in the ¼ cup fresh Key lime juice (for cake), 1 teaspoon lime zest, and 1 teaspoon vanilla extract (for cake) until evenly distributed.
Step 7: Pour the batter into the prepared Bundt pan, spreading it evenly. Bake for 1 hour and 15 minutes to 1 hour and 30 minutes, or until a wooden skewer inserted into the center comes out clean. Let the cake cool in the pan for 15 minutes before inverting it onto a wire rack to cool completely.
Step 8: While the cake cools, prepare the glaze. In a small bowl, whisk together the 1 cup powdered sugar, 2 tablespoons Key lime juice (for glaze), and ½ teaspoon vanilla extract (for glaze) until smooth. If the glaze is too thick, add a tiny bit more lime juice; if too thin, add a little more powdered sugar.
Step 9: Once the cake is completely cool, drizzle the Key lime glaze over the top, allowing it to drip down the sides. Let the glaze set before slicing and serving.