Prepare a parchment-lined cookie sheet and heat the oven to 350°F. The parchment should lie flat beneath the dough portions.

Stir the sugar, milk, melted butter, peach schnapps, peach nectar, baking powder, salt, and eggs together in a large mixing bowl. Aim for an evenly blended mixture without visible streaks of egg.

Add the flour in stages, stopping the stirring as soon as it disappears into the dough. The finished dough will be soft and sticky rather than stiff.

Coat your palms with nonstick cooking spray, shape 1-tablespoon scoops into smooth balls, and bake them on the prepared sheet for 14 to 15 minutes. Look for lightly golden undersides and pale tops that have just set.

After 2 to 3 minutes of cooling, cut a 1-inch hollow into each flat underside with a sharp paring knife, then let the shells cool completely. The warm crumb should cut more readily than a fully cooled center, with cookie left around the cavity to support the filling.

Beat the butter with vanilla and salt, work in the powdered sugar gradually, and fold the peach preserves through the frosting. The buttercream should look fluffy and hold a soft mound rather than flow.

Fill each cavity lightly, coat the flat surfaces with a thin layer of buttercream, and join the cookie halves in pairs. The edges should meet neatly without a thick ring of filling squeezing out.

Blend the decorating nectar with vanilla, split it equally between two bowls, tint one red and the other yellow, and put the sugar in a separate bowl. The two liquids should show distinct colors before you begin brushing.

Brush opposite sides of each assembled cookie with red and yellow nectar, roll it in sugar, and refrigerate under plastic wrap for 8 hours or overnight. The sugar should cling as visible crystals, and the chilled shells will soften as the moisture moves into the crumb.

Add a mint or basil leaf just before serving, if desired. A fresh green leaf completes the peach-like appearance without becoming a required garnish.