For the pastry cream: Whisk together 1 1/2 cups of the milk, 1/4 cup of the sugar and the salt in a medium saucepan. Bring to a simmer over medium heat, whisking until the sugar is dissolved.
Meanwhile, whisk the cornstarch and egg yolks with the remaining 1/2 cup milk and 1/4 cup sugar in a medium bowl until smooth. Ladle about 1/2 cup of the hot milk mixture into the bowl while whisking, then add all of the mixture back to the saucepan. Bring to a boil, whisking constantly; let boil until thickened, about 2 minutes. Strain through a fine-mesh sieve into a bowl, then stir in the preserves, schnapps and almond extract. Cool the pastry cream slightly, then cover the surface directly with plastic wrap and refrigerate until cold.
For the cookies: Position an oven rack in the middle of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment.
Whisk together the flour, baking powder and salt in a medium bowl. Whisk together the sugar, milk, butter, nectar, schnapps and eggs in a large bowl. Add the flour mixture and beat with a wooden spoon until smooth to make a thick, sticky dough.
Lightly grease your hands with the oil and roll tablespoons of the dough into balls, arranging them about 1 1/2 inches apart on the lined baking sheets. Bake one sheet at a time, until the undersides of the cookies are golden and the tops are just set, about 15 minutes. Cool just a few minutes. While the cookies are still warm, use a sharp paring knife to cut an approximately 1-inch-wide teaspoon-sized divot into the flat side of each cookie (be careful not to pierce the tops or sides of the cookies). Bake the other sheet of cookies and cut out the divots. Cool the cookies completely.
Spoon a heaping teaspoon of pastry cream into each cookie, then sandwich 2 similar-looking ones together to make a peach shape, cleaning off any pastry cream that squeezes out of the seams. At this point, the cookies may not stick together very well; prop them up next to each other to keep their shape.
For decorating: Combine the nectar and almond extract in a small bowl and add enough food coloring to make it bright red, about 8 drops. Put the sugar in another bowl.
Working one at a time, paint each peach cookie all over with the red nectar mixture using a medium paintbrush, then roll in the sugar to coat thoroughly. Make sure the cookies are still nicely sandwiched and place in a 9-by-13-inch baking pan (the cookies should fit snugly in the baking pan so that they keep their shape). Cover the dish with plastic and refrigerate 8 hours and up to overnight (this will blend the flavors and also set the pastry cream to keep the cookies together).
Just before serving, garnish each cookie with a clove and mint sprig to look like little stems.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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