In a large bowl, cream together the softened butter, sugar, brown sugar, and instant lemon pudding mix at high speed for 1 minute. Add the eggs, lemon zest, lemon juice, and vanilla extract, and continue mixing until fluffy.

In a separate bowl, whisk together the flour, baking soda, and poppy seeds. Add to the creamed butter mixture and mix at low speed until combined. Using a cookie dough scoop, scoop all the cookie dough onto a pan lined with parchment paper. Cover and refrigerate for at least 30 minutes.

Preheat the oven to 350℉. Line a few baking sheets with parchment paper. Arrange the chilled scoops of cookie dough on the prepared pans, leaving 2 inches between each cookie for spreading room. Bake, one pan at a time, in the preheated oven for 10-14 minutes or until slightly golden around the edges. Let cool on the pan for 5 minutes before transferring to a wire rack to finish cooling while you bake the rest of the cookies.