Preheat oven to 150 C / Gas 2. Grease several baking trays.
Beat the eggs, caster sugar and dark brown soft sugar in a bowl until the sugar is incorporated, then beat in lemon juice, almonds, baking powder, cinnamon, ginger, black pepper, allspice and cloves until thoroughly combined. Mix in flour to make a sticky dough.
Turn the dough out onto a well-floured work surface and knead the dough 1 to 2 minutes, adding more flour if needed, to make a smooth workable dough. Pinch off pieces of dough and roll them into balls about 3.75cm diameter; place the balls on the prepared baking trays at least 2.5cm apart.
Bake in the preheated oven until a cocktail stick inserted into the centre of a cookie comes out clean, about 25 minutes. Remove from trays immediately to cooling racks to prevent cookies from getting too hard.
Stir together icing sugar and water to make the glaze; drizzle each cookie while slightly warm with about 1/2 teaspoon, spreading it around the top of the cookie.