Preheat your oven to 350°F (180°C). Line two baking sheets with parchment paper to ensure the cookies don't stick. The proper temperature is essential for achieving the right texture - not too soft but not overly crisp either.

In a large bowl, cream together the softened butter, powdered sugar, and fresh lemon zest until light and fluffy. This forms the base of your tender cookie. Add the egg and mix until well incorporated. Then mix in the vanilla extract and sour cream, which will add moisture and richness to the final cookies.

In a separate medium bowl, whisk together the flour, baking powder, and salt to ensure even distribution. With your mixer on low speed, gradually incorporate the flour mixture into the butter mixture until just combined. Avoid overmixing to keep the cookies tender.

Lightly grease your hands with softened butter or oil to prevent sticking. Scoop approximately 1 tablespoon (15g) of dough and shape into uniform balls. Place these balls on the prepared baking sheets, leaving space between them for slight spreading.

Gently flatten each ball slightly with your palm. Bake for 13-15 minutes until the bottoms are lightly golden brown but the tops remain pale. Remove from the oven and allow to cool completely on the baking sheets before handling.

Once cooled, use a small sharp knife to carefully hollow out the center of each cookie. Place these removed crumbs in a separate bowl as they will be an important part of the filling.

Break the reserved cookie centers into fine crumbs. Add peach jam and ground nuts (pecans, walnuts, or almonds) to the crumbs and stir until thoroughly combined. This creates a flavorful, sweet filling with a slight textural contrast.

Transfer the filling mixture to a piping bag fitted with a plain 9mm tip. Pipe the filling into the hollowed cookies, then pair them together to create sandwich cookies. Press gently to secure without breaking.

In one small bowl, combine half the peach liqueur with yellow food coloring. In another bowl, combine the remaining liqueur with red food coloring. Place fine sugar in a third bowl. Dip each sandwiched cookie first into the yellow liqueur, then partially into the red liqueur to create a peach-like gradient. Let excess liquid drain briefly.

While still wet from the liqueur, roll each cookie in the fine sugar to coat evenly. This creates the characteristic fuzzy appearance of a real peach and adds a pleasant textural element.

Arrange the finished peach cookies on a serving platter and decorate with small green leaves (mint leaves work well) to mimic peach stems. Allow the cookies to fully set before serving for the best texture and appearance.