• Preheat oven to 325°F (165°C) with a rack in the middle position. Grease and flour a 9-inch round cake pan.

Peach Cobbler Topping

• Place the peeled, sliced peaches in a bowl.
• Add the light brown sugar, granulated sugar, allspice, and salt.
• Gently mix to coat the peaches. Set aside.

Mix Dry Ingredients

• In a separate bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.

Cream Butter and Sugar:

• In a stand mixer with a paddle attachment (or use a large bowl and hand mixer), beat the butter on medium-high speed until creamy (about 1 minute).
• Add the granulated sugar and vanilla extract. Mix on low to combine, then increase to medium-high and beat until light and fluffy (about 5 minutes).
• Scrape the sides and bottom of the bowl as needed.

Add Eggs

• Reduce mixer speed to medium-low. Add the eggs and egg yolks, one at a time, beating just until each is incorporated.
• Scrape the sides and bottom of the bowl.

Combine Wet and Dry Ingredients:

• Add one-third of the flour mixture to the butter mixture and mix on low until just combined.
• Add half the sour cream and mix until just combined.
• Repeat with another third of the flour, then the remaining sour cream, then the last third of flour.
• Scrape the sides and bottom of the bowl.
• Tip: Don’t overmix, stop as soon as the ingredients are incorporated and no flour streaks remain.

Assemble the Cake:

• Spoon the peach mixture evenly into the bottom of your prepared cake pan.
• Pour the cake batter on top and smooth the top with a spatula.
• Bake for 55–65 minutes, or until the cake is no longer jiggly and a toothpick inserted into the center comes out clean or with just a few moist crumbs.
• Let the cake cool in the pan for 20 minutes.
• Run a knife around the edge, then carefully flip it onto a serving plate.
• If any peaches stick to the pan, simply lift them out and place them back on top of the cake.

Brown Butter Icing

• Place the butter in a light-colored skillet over low heat.
• Let it melt, stirring occasionally.
• Once melted, increase the heat to medium and continue to cook, stirring occasionally. The butter will begin to foam and develop a nutty aroma.
  
• After 5–8 minutes, you’ll notice brown bits forming at the bottom of the pan and the butter will turn golden brown.
• Remove from heat and let it cool for 5 minutes.
• Whisk in the confectioners’ sugar, milk, and vanilla until smooth.
• If the glaze is too thick, add a little more milk. If it’s too thin, add more sugar.
• Drizzle the icing over the slightly warm cake.