Make the flax egg: combine the ground flax and cold water in a small bowl. Stir with a fork until combined. Leave the mixture to rest for at least 10 to 15 minutes, until gooey and thick.
Preheat the oven to 350°F (180°C).
In a large bowl, add the flour, baking powder, salt, all the spices and whisk to combine.
Make a well in the flour mixture and add the vegan butter, sugar, and flax egg. Rub in with your fingertips until the mixture resembles fine breadcrumbs.
Add the molasses and orange zest. Mix to a firm dough.
Knead the dough briefly and gently on a floured surface for a few minutes. (if necessary, you can put a little flour on your hands too).
Cover the dough in plastic wrap and rest in the fridge for at least 2 hours.
On a generously floured surface, roll the dough out to 1/4 inch (6mm) thick. Cut out the cookies, dipping your cookie cutter in flour each time to get sharp edges. Move the gingerbread cookies to a parchment-lined baking tray. Repeat with the leftover dough.
Bake for 10-12 minutes. Allow to cool completely before decorating.
When you are ready to decorate, make the icing: Mix the lemon juice and oat milk with the confectioners' sugar. The icing should be thick but pourable and should hold its shape.
Transfer the icing to a decorating pen (or a piping bag fitted with a fine nozzle) and decorate the cookies as you like.
Leave the cookies to dry flat for at least 2 hours before storing in an airtight container.