Put the mastic tears and 1 tablespoon of granulated sugar in a mortar. Grind for 2 to 3 minutes, until you have a fine powder with no chunks. Don't grind the mastic alone, because it warms up and turns into a sticky clump.
In a mixing bowl, beat the softened butter and 90 g of powdered sugar with a mixer for 3 to 4 minutes, until pale and fluffy. Add the egg yolk, vanilla, and mastic sugar and beat until smooth.
Add the flour and salt and mix on low speed until no dry flour is left and the dough comes together. It will be soft. Cover and chill for 30 minutes, until firm enough to shape without sticking to your hands.
Heat the oven to 165 C / 325 F and line two 33 x 46 cm / 13 x 18 inch sheet pans with parchment. Roll the dough into 24 balls of about 25 g each, a heaped tablespoon. Place 12 on each pan and press each one to about 1.5 cm / 1/2 inch thick.
Bake both pans together on the middle and lower racks for 14 to 16 minutes, swapping their positions halfway. The cookies are done when the bottoms are light golden and the tops are pale and set. Don't wait for the tops to brown.
Cool the cookies on the pans for 10 minutes. Roll each warm cookie gently in the 60 g of powdered sugar until coated, then move it to a wire rack. Dust a little extra over the top through a sieve if you like.