Make the batter: Combine softened butter, white sugar, and vanilla extract. Beat using an electric hand mixer on low speed to break apart big clumps. Increase to medium speed and beat until smooth and airy, about a few minutes. Add the eggs one at a time, and beat for 1 minute on medium speed after each. Add flour and milk to the mixture, and beat on low speed until combined, about a few minutes. Increase to medium speed and beat for another 5 minutes. Lastly, add diced apples and use a spatula to stir them into the mixture until mixed.
Bake: Scoop the batter into a buttered 9x5 inch loaf pan. Smooth out the surface using a spatula. Bake at 350 F for 60 minutes. A toothpick inserted into the center of the pound cake should come out clean when it’s done. Run a knife along the edges of the pound cake to loosen it from the pan. Let cool for 10 minutes and carefully remove from the loaf pan.
Make the caramel glaze: Combine and mix brown sugar and flour in a small saucepan, breaking apart any large clumps of brown sugar. Add butter and milk, and turn the burner on to medium heat. Stir the mixture as the butter melts. Then bring to a boil over medium-high heat, and let it boil for 1-2 minutes. Remove from heat and stir in vanilla extract. Continue stirring until the glaze is smooth and thick, about a few minutes. Pour the glaze over the pound cake. Transfer to the refrigerator to cool and harden.