Whisk eggs and egg yolks together in medium bowl and set aside.
Mix lemon juice, sugar, and salt together in a small heavy saucepan and heat over medium heat until sugar is dissolved but not yet boiling, stirring frequently. SLOWLY drizzle this into the whisked eggs, whisking constantly until combined.
Pour back into the saucepan and return to medium heat. Stir constantly until the mixture has thickened, about 3-5 minutes.
Turn off the heat and gently whisk in butter until melted, then whisk in the milk. Strain through a fine mesh strainer and let cool to room temperature.
Pour into your popsicle molds of choice and freeze. Meanwhile prepare the shortbread cookie crumble.
Take popsicles out of the freezer when frozen, and remove from the molds. Let sit to soften just for a minute before coating with the shortbread crumbs. Eat and enjoy!
Preheat the oven to 350° F and prepare an 8X8 inch square pan by greasing it with butter.
Sift confectioners’ sugar and flour into the bowl of a stand mixer. Mix on low speed for a few seconds to mix together. Add the butter and return to low speed until the dough comes together smoothly, scraping sides of the bowl as necessary.
Pour out dough into your prepared pan and press with hands or the flat side of a cup until the dough covers the bottom, about 1/4 inch thick. Prick several times with a fork.
Bake for 20-25 minutes in the oven until golden brown. Let cool in the pan on a wire rack.
Break the shortbread up and smash into crumbs with a rolling pin or flat side of a cup.