Preheat the oven to 350°F (175°C) and grease the cake pan.
In a mixing bowl, combine the softened butter and granulated sugar, and cream them together until they become light and fluffy.
Add the eggs to the mixture, one at a time, ensuring to beat well after adding each one.
Add and combine the flour and baking soda, in a separate bowl.
Gradually incorporate the flour mixture into the butter mixture, alternating with the buttermilk. Begin and end with the flour mixture.
Stir in the vanilla extract and chopped orange slices.
Pour the prepared batter into the greased cake pan, ensuring to spread it evenly and smoothing the top using a spatula.
Bake for approximately 45-50 minutes or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the orange glaze. In a saucepan, heat the orange juice over medium heat until it comes to a simmer.
Take the saucepan off the heat and whisk in the powdered sugar until it is smooth and well combined.
After the cake is fully baked, take it out of the oven and transfer it onto a cooling rack. Let it rest in the pan for 10 minutes to cool down.
Carefully invert the cake onto the cooling rack and remove the pan. Let it cool completely.
Drizzle the orange glaze over the cooled cake, allowing it to drip down the sides.
Slice and serve the Brenda Gantt Orange Slice Cake to your delighted guests.