In a medium bowl, measure out flour, baking soda, and salt, and gently combine.
Add softened butter and sugar to a separate bowl, and cream together for 1-2 minutes. The mixture will be crumbly and easily fall apart.
Add 1 egg, and mix until combined. Then add the second egg along with vanilla extract, lemon juice, lemon zest, and poppyseeds. Mix until combined.
Begin to sift in your flour mixture, and for best results work in 4 batches. Be careful to not over mix as this can result in a drier dough.
Once all of the flour is folded in, cover the bowl with a lid or saran wrap, and let it chill in the fridge for at least 1 hour.
While the dough is chilling, prepare the lemon icing by combining all of the ingredients in a medium bowl. The icing will keep in the fridge for up to 3 days.
Once ready to bake cookies, preheat oven to 350°.
Grease a 9x13-inch baking sheet, and top with parchment paper. Scoop 2-3 tablespoons of cookie dough for each cookie, and form into evenly sized balls.
Working in batches of 6 cookies per sheet, bake for 12 minutes. Allow to cool fully for about 20 minutes before drizzling with icing.