For the cookies, prepare the vegan eggs and set aside for at least 5 minutes. Add the flour, baking powder, and baking soda to a mixing bowl and whisk to combine. Set aside.
In a stand mixer fitted with a paddle attachment, cream together butter and sugar 2 to 3 minutes on medium speed. Add vanilla, vegan eggs, and sour cream. Mix until well combined.
Slowly add dry ingredients with the wet, a cup at a time, until well combined. Transfer the dough to a clean surface dusted with flour and shape into a log that is 12 inches long and 2- 2 ½ inches in diameter. Roll on the surface to create the log shape and smooth out the sides. Wrap with plastic wrap and chill in the fridge for 8 hours or overnight.
Preheat oven to 425 degrees and line baking sheet with parchment paper.
Remove the chilled dough from the plastic wrap and place it on a floured surface. Slice into ⅓-inch-thick rounds, taking care to maintain their shape.
Arrange the slices on a baking sheet, spacing them at least an inch apart. Bake for 5 to 6 minutes, or until the bottoms are lightly golden. Keep a close watch to prevent overbaking. Transfer the cookies to a cooling rack and allow them to cool completely before frosting.
For the frosting, use a stand mixer with a paddle attachment or mix by hand to cream together the butter and cream cheese. Add the vanilla, lemon, salt, and confectioners' sugar, one cup at a time, mixing until smooth and the desired consistency is reached. If the frosting is too thin, add more sugar until desired consistency is reached. If the frosting becomes too thick, thin it out with a small amount of nondairy milk.
Frost the cooled cookies and top with vegan sprinkles, if using. I like to keep these stored in the fridge for optimal freshness but you can leave them out at room temperature if you prefer, and also when serving for a gathering, you just want to be sure the frosting is firm enough to stay out at room temperature.