Preheat your oven to 350°F (175°C) and grease your baking pan to prevent sticking.
Toss the sliced peaches with brown sugar and let them sit for a few minutes until the juices begin to release and form a syrup.
In a large mixing bowl, whip together the softened butter and granulated sugar using a mixer until the mixture is light and fluffy, and smells subtly sweet.
Add the eggs one at a time, beating well after each addition to ensure they fully incorporate into the batter.
Mix in the vanilla extract, and then gradually fold in the flour until just combined, avoiding overmixing to keep the batter tender.
Gently fold in the caramelized peach slices, allowing some syrup to swirl into the batter for extra flavor and moistness.
Pour the batter into your prepared baking pan, smoothing the top with a spatula and spreading the peaches evenly throughout.
Bake in the preheated oven for about 60 minutes, or until the center is set and a toothpick inserted into the middle comes out clean.
While baking, the house will fill with a warm, fruity aroma, and you'll see the edges turn a lovely golden brown.
Remove the cake from the oven and let it cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.
Slice the cake and serve it warm or at room temperature, enjoying the tender crumb and the rich, caramelized peaches inside.
