Begin by preheating your oven to 300°F (149°C) and place a clean baking sheet in the refrigerator to chill. While the oven heats, gather a large bowl and combine 1¼ cups arrowroot flour, ¼ cup powdered sugar (or superfine caster sugar), and ¼ teaspoon salt, mixing them well until evenly distributed. In a separate small bowl, mix together ¼ cup cooled melted butter, 1 duck egg (or 1 regular egg plus 1 yolk), and ½ teaspoon vanilla extract until well combined.

Pour your wet mixture into the bowl with the dry ingredients and mix thoroughly. The dough should feel like soft mashed potatoes – if it's too stiff, add milk one teaspoon at a time until you reach the right consistency. Take your cookie press and fill it with the dough following the manufacturer's instructions.

Remove the chilled baking sheet from the refrigerator and, leaving it unlined, begin pressing out your cookies directly onto it. The cold surface helps the dough stick better. Leave some space between each cookie, though they won't spread much during baking.

Place the sheet in your preheated oven and bake for 15 minutes. The cookies should remain pale – if you prefer them slightly golden, add baking time in 2-minute intervals until you reach your desired color. Once done, let them cool on the baking sheet for 10 minutes – they'll slide off easily. Transfer to a wire rack to cool completely.

Store your finished cookies in an airtight container or cookie tin, where they'll stay fresh for up to a week. The recipe yields about 36 delicate, melt-in-your-mouth cookies perfect for serving with hot tea or coffee.