In a medium sized mixing bowl, blend together the flour, butter, sour cream and brown sugar until thoroughly combined. Dough will be stiff. Divide dough in half. Cover and chill for 3 hours in the refrigerator.
Preheat the oven to 350 degrees.
Lightly flour your working surface, then roll out each half of the dough to a 1/8 inch thickness. Using a 2 inch round cookie cutter, cut the dough into rounds.
Then using a 1 inch round cutter, cut out the centers from half of the rounds.
Lightly brush water over the cookies with the holes cut in them, then place them wet side down on top of the cookies without the holes.
Place the cookies 1 inch apart on ungreased baking sheets.
Combine the 3 Tablespoons of sugar with 1 Tablespoon of water and using a pastry brush, brush the tops of the cookies.
Spoon 1/2 teaspoon pineapple jam into the center of each cookie then place one half a maraschino cherry over the pineapple jam in the center.
Sprinkle the cookies with the chopped pecans.
Bake the cookies at 350 degrees for 15 to 20 minutes or until the edges are lightly browned.
Cool completely on a wire rack.
Mix together 1/2 cup sifted confectioners sugar with milk until the the icing is smooth and of a drizzling consistency.
Drizzle icing over the tops of the cookies and serve.