Preheat oven to 175°C / 350°F. Line two baking sheets with parchment paper or silpat. Set aside.
Soften the butter: There are 2 ways you can do this.
a) Start with room-temperature butter for best results. Place the butter in a heatproof bowl and set it over a pot of simmering water. When a little bit of butter has melted, remove the bowl from the pot of water and use a wire whisk to whisk vigorously to mix all the butter together. Repeat until the butter is soft.
b) Microwave the butter at 70 to 80% power for 30 seconds, then at 15 seconds interval. You want the butter to be soft like a toothpaste consistency and shiny-looking.
If you have softened the butter too much until it liquefies, stick the bowl of butter into the freezer for 3 to 5 minutes and the consistency should be just right.
190 grams unsalted butter
Once you have your soft butter, transfer the butter into a mixing bowl. Sift in the icing sugar and whisk with a wire whisk gently until incorporated - do not whisk vigorously as you do not want to incorporate too much air inside.
80 grams icing sugar
Whisk in the fleur de sel, followed by vanilla and egg white. Again, whisk gently so that you don't incorporate too much air inside
2 pinches fleur de sel, ½ teaspoon vanilla, 30 grams egg white
Sift in the flour and use a spatula to mix in the flour until incorporated. Stir in the milk.
225 grams all-purpose flour, 2 tablespoons milk
Transfer the cookie dough into a piping bag fitted with a big open/close star piping tip (for the ♥, use a a small open star piping tip) and pipe the dough onto the lined baking sheets. It's best to pipe the same shape on the same baking sheet so the cookies bake evenly. If the shape didn't come out nicely, you can always scrape it up with a spatula and try again. (If the batter is too stiff, it will not be easy to pipe a clean shape. Microwave the batter for 5 seconds so that the batter soften a little. If the batter is in the piping bag, use your hands to massage the batter so that the heat of your hands soften the batter.)
Once the cookies are piped, bake them in the preheat oven for 15 minutes (start checking on them every minute after 10 minutes of baking), until the edges are lightly golden (I personally prefer them to be baked 2 to 3 minutes longer, so total baking time of 18 minutes for me).
Let the cookies cool on the baking sheet for 3 minutes, then slide the parchment paper/silpat onto a rack and let the cookies cool to room temperature completely. Store the cookies in an airtight container for up to 2 weeks.
NOTES
Use only the best butter - I highly recommend Elle&Vire, one of my favourite French butters that can be found in baking shops and major supermarkets.
If you want to make the batter in a stand mixer, combine the softened butter, sifted icing sugar, fleur de sel, vanilla and egg white in the mixing bowl. Use a paddle attachment and mix on medium speed until combined. Sift in the flour and mix on low speed until just combined then mix in the milk/water. Use a spatula to finish mixing by hand.
No fleur de sel? Replace with 1 pinch of fine sea/table salt.