Preheat your oven to 325°F (165°C). Grease and flour a 10-inch bundt or tube pan, ensuring all crevices are coated.

In a large mixing bowl, cream the butter, shortening, and sugar together until light and fluffy, about 3-5 minutes.

Add the eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl to ensure all ingredients are evenly incorporated.

In a separate bowl, sift together the flour, baking powder, and salt.

Gradually add the dry ingredients to the butter mixture, alternating with the milk. Begin and end with the dry ingredients, mixing on low speed to avoid overbeating.

Stir in the vanilla extract until just combined. Pour the batter into the prepared pan, smoothing the top with a spatula.

Bake for 1 hour and 15 minutes to 1 hour and 30 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 10 minutes before turning it out onto a wire rack to cool completely.

In a medium saucepan, melt the butter over medium heat.

Add the brown sugar and salt, stirring until the mixture is smooth and bubbly. Let it cook for 2 minutes, stirring constantly.

Slowly whisk in the milk and bring the mixture to a boil. Remove from heat and let it cool for 5 minutes.

Gradually add the powdered sugar, whisking until smooth. Stir in the vanilla extract.

While the icing is still warm, pour it over the cooled pound cake, allowing it to drip down the sides. Use a spatula to spread it evenly if necessary.