Preheat the oven to 350°F (175°C).
In a mixing bowl, combine all-purpose flour and baking powder along with the spices: ginger, cinnamon, cloves, and nutmeg.
In a separate bowl, mix together brown sugar, honey, applesauce, and the egg until well combined.
Gradually add the dry mixture to the wet mixture. Stir just until combined.
Fold in the chopped nuts, ensuring they are evenly dispersed throughout the dough.
Cover the dough and refrigerate for at least 30 minutes.
Using a spoon, scoop small amounts of dough and shape them into balls. Place them on a lined baking sheet.
Bake the cookies for 10-12 minutes, or until they are lightly golden around the edges.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack.
For the icing, mix powdered sugar with lemon juice until smooth, then drizzle over the cooled cookies.
Let the icing set for a short while before serving or storing the cookies.