Preheat your oven to 350°F (175°C) and line a large baking sheet with parchment paper.

In a large mixing bowl, whisk together the melted vegan butter, brown sugar, granulated sugar, non-dairy milk, cornstarch, vanilla extract, cinnamon, baking soda, and salt until smooth and well combined. Using a rubber spatula or wooden spoon, fold in the flour until a soft, cohesive dough forms.

On the prepared baking sheet, sprinkle about ½ teaspoon of brown sugar in small mounds, spaced apart for each cookie. Layer 4–5 thin slices of peach over each brown sugar mound. Scoop about 1½ tablespoons of cookie dough and place it directly on top of the peach slices. Gently press the dough down with your palm to help it stick to the peaches.

Repeat the process with the remaining dough and peach slices, ensuring enough space between cookies to allow for spreading. Bake for 12–13 minutes, or until the edges are golden and the centers are just set.

While the cookies are still warm, use a large round cookie cutter or the rim of a cup to gently swirl around each cookie, shaping them into neater circles. Let them cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely. Enjoy!