Chop the butter into small pieces. Mix the butter, honey and sugar in a saucepan. Heat, stirring constantly, until the sugar has dissolved. Pour into a large mixing bowl and cool. Add the almonds, 400 grams (approximately 14 ounces) of flour, ginger, lemon zest and egg. Knead well, adding flour, if necessary. Mix the baking soda with the rum and pour into the dough. Knead until the dough is no longer sticky.
Cover the bowl with plastic and chill overnight.
Preheat the oven to 180°C (approximately 350°F). Line a baking sheet with parchment paper.
Roll out the dough on a floured surface. Use cookie cutters to cut out shapes. Place the cookies on the baking sheet and bake for 15-20 minutes, until golden brown. Remove from the baking sheet and cool on a wire rack. Serve warm.