Preheat your oven to 325°F (165°C). Thoroughly grease and flour a 10-inch bundt pan, ensuring every crevice is covered.
In a medium saucepan, combine diced peaches, brown sugar, lemon juice, cinnamon, and nutmeg. Simmer over medium heat for 5-7 minutes until peaches soften slightly and release their juices. Sprinkle cornstarch over the mixture and stir constantly for 1-2 minutes until thickened. Remove from heat and let cool while preparing the cake batter.
In a stand mixer fitted with the paddle attachment, beat the softened butter until creamy (about 1 minute). Gradually add the sugar and beat on medium-high speed for 5-7 minutes until the mixture is light and fluffy.
Add eggs one at a time, beating well after each addition. Scrape down the sides of the bowl frequently to ensure even incorporation.
In a separate bowl, whisk together flour, baking powder, and salt.
With the mixer on low, add the flour mixture to the butter mixture in three additions, alternating with milk (begin and end with flour). Mix just until combined after each addition.
Stir in the vanilla and almond extracts until just combined.
Pour one-third of the batter into the prepared bundt pan. Spoon half of the peach mixture over the batter, keeping it away from the edges of the pan. Top with another third of batter, the remaining peaches, and finally the remaining batter.
Use a knife to gently swirl the batter and peaches together with 2-3 gentle passes.
Bake for 70-75 minutes, or until a wooden skewer inserted in the center comes out clean. If the top browns too quickly, tent loosely with aluminum foil after 45 minutes.
Allow the cake to cool in the pan for exactly 15 minutes. Invert onto a wire rack and cool completely before glazing.
Whisk together powdered sugar, peach nectar or milk, and vanilla extract until smooth. The glaze should be thick yet pourable—adjust consistency with additional liquid or sugar as needed. Drizzle over the cooled cake, allowing it to cascade down the sides.