Preheat oven to 350°F. Line two baking sheets with parchment.
Beat butter, granulated sugar, brown sugar, and lemon zest until pale and fluffy, about 2 minutes.
Mix in egg yolks, heavy cream, lemon juice, and vanilla until smooth.
Whisk flour, baking powder, baking soda, and salt in a bowl.
Add dry ingredients to the wet mixture. Stir just until a soft dough forms.
Scoop 1½-tablespoon portions, roll into balls, and set 2 inches apart. Gently flatten tops.
Bake 9–11 minutes until edges look set and centers are pale. Do not overbake.
Cool on the sheet 5 minutes, then move cookies to a rack to cool completely.
Whisk powdered sugar, lemon juice, heavy cream, and vanilla into a thick, glossy glaze.
Spoon glaze over cooled cookies and spread to the edges. Let set 10–15 minutes.
Sprinkle a thin, even layer of granulated sugar over each glazed cookie.
Torch the sugar until amber and glassy. Alternatively, broil briefly, watching constantly.