In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until well combined.

Prepare the lemon sugar by combining 1/3 cup sugar with 1 teaspoon of the lemon zest in a small bowl; rub together with fingertips until fragrant and set aside.

In a stand mixer fitted with a paddle attachment, cream the softened butter, 1 1/4 cups sugar, and the remaining lemon zest on medium-high speed for 3 to 4 minutes until light and fluffy.

Add the egg and egg yolk one at a time, beating well after each addition to ensure proper emulsification.

Mix in the fresh lemon juice and vanilla extract on low speed.

Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined; do not overmix.

Cover the dough and refrigerate for at least 60 minutes to control spread and hydrate the flour.

Preheat the oven to 350°F (175°C) and line two large baking sheets with parchment paper or silicone mats.

Scoop approximately 1.5 tablespoons of dough per cookie and roll into smooth spheres.

Roll each dough ball in the prepared lemon sugar until evenly coated and place on the baking sheets 2 to 3 inches apart.

Bake for 10 to 12 minutes until the edges are set and very lightly golden, ensuring the centers remain soft and slightly puffed.

Cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.