Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan, or line the bottom with parchment paper for easier removal.

In a large mixing bowl, cream together the softened butter and ¾ cup of granulated sugar using an electric mixer on medium speed until light and fluffy, about 3-4 minutes. This incorporates air into the batter, making the cake tender.

Add the eggs one at a time, mixing well after each addition. Then, mix in the vanilla extract.

In a separate bowl, whisk together the sifted flour, baking powder, baking soda, and salt.

Gradually add the dry ingredients to the wet mixture, alternating with the milk. Start and end with the flour mixture. Mix until just combined; do not overmix to keep the cake light.

In a medium bowl, toss the sliced peaches with lemon juice, brown sugar, and cinnamon. This enhances the flavor of the peaches and helps to soften them during baking.

Pour half of the cake batter into the prepared cake pan. Spread half of the peach mixture over the batter. Then, pour the remaining batter on top and finish with the remaining peaches.

Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean. The baking time may vary based on your oven, so keep an eye on it.

Once baked, remove the cake from the oven and allow it to cool in the pan for 10 minutes before transferring it to a cooling rack to cool completely.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Adjust the milk as needed to achieve your desired consistency.

Once the cake is completely cool, drizzle the glaze over the top for added sweetness and decoration.