In a heatproof bowl, microwave or warm the butter until it's melted (be sure it doesn't sputter or you'll lose some necessary fat for the dough).
Add the granulated sugar and the brown sugar, salt and vanilla and whisk until the the mixture is thick and shiny (the butter won't look separated).
Add the egg and yolk and whisk for another 2-3 minutes.
Add the dry ingredients to the wet and stir with a spatula until just combined.
Set the dough, covered with plastic wrap, in the fridge for 20-30 minutes.
Preheat oven to 350 F. Line two cookie sheets with parchment paper.
Pour the sugar for rolling into a small bowl and set aside.
Drop the cookie dough into 1 ½-2 tablespoon rounds on the parchment paper, leaving a generous amount of space between them.
Dip the dough mounds in the granulated sugar rolling gently to cover the dough in sugar. Return to cookie sheet.
Bake for 10 minutes. When you remove them from the oven they will be puffy and cracked, as they cool they flatten.
Store in an air-tight container, to avoid the cookies drying out.