For the Lemon Pastry Cream:

1. Heat milk in a saucepan over medium-low heat until steaming, then reduce heat to low.
2. In a bowl, whisk together egg yolks, sugar, lemon zest, salt, vanilla, and cornstarch until smooth.
3. Gradually add heated milk to egg mixture, whisking constantly.
4. Transfer mixture back to saucepan and cook over medium-low heat until thickened, stirring continuously.
5. Remove from heat, stir in butter, cover with plastic wrap, and chill in the fridge.

For the Lemon Sugar:

1. Combine sugar and lemon zest in a bowl, then set aside.

For the Lemon Sugar Cookies:

1. Preheat oven to 350°F (175°C) and line two cookie sheets with parchment paper.
2. In a bowl, whisk together flour, baking powder, baking soda, and salt, then set aside.
3. Cream together butter and sugar until fluffy, then mix in egg, vanilla, and lemon zest.
4. Gradually add dry ingredients to wet ingredients, mixing until dough forms.
5. Roll dough into balls, coat in lemon sugar, and flatten slightly on prepared cookie sheets.
6. Bake for 9-10 minutes, then cool on a wire rack.

Assembling the Cookies:

1. Pipe pastry cream onto cooled cookies, sprinkle with granulated sugar, and brûlée until golden brown.
2. Allow cookies to cool for 10 minutes before serving. Enjoy immediately for the best texture and flavor!