Begin by heating the lemon juice over high heat*. Bring the lemon juice to a boil; then reduce the heat to medium. Cook until you have approximately 2 tablespoons of lemon juice. Remove from the heat and stir in the butter until melted. Set aside to cool.
In a large bowl, whisk together the flour, baking soda, and salt. Set aside.
In a medium bowl, combine the egg, egg yolk, sugar, lemon zest, and vanilla. Once the butter and lemon juice mixture is slightly cool, stir it in. Then, add the wet ingredients to the prepared dry ingredients and stir until just combined.
Cover and chill for 45 minutes.
On a floured surface, roll out the dough (1/3 at a time) to a 1/8-inch thickness. Use a 2.5-inch round cookie cutter to cut out cookies. Place the rounds on a parchment-lined baking sheet about an inch apart. Bake the cookies for 6-7 minutes or until they just start to lightly brown. (Keep an eye on them as they brown rather quickly.) Let the cookies cool on the baking sheet for 2-3 minutes and then transfer them to a cooling rack. Once cooled completely, the cookies can be stored in an airtight container.