Preheat oven to 350 °F (check that you have an oven rack in the middle position) and line two cookie sheets with non-stick parchment paper or silicon baking sheets.
Combine flour, 1 1/2 teaspoons baking powder, and salt in a medium sized bowl.
Wash your lemons well and dry them with a paper towel, then zest them directly over the bowl of flour (reserve the lemons for other uses).
Use a sharp pointy knife to split your vanilla bean lengthwise and scrape the seeds and add to the flour mixture (reserve the pod shell for other uses).
Whisk the flour mixture well and set aside.
Beat the butter and sugar together until they are combined and look fluffy (2-3 minutes using a stand mixer, 5 minute with a hand mixer), scraping down the sides of the bowl as needed.
Combine the oil, water, and 2 teaspoons of baking powder in a small bowl and add to the butter and sugar mixture, add the lemon extract, and mix on low speed until combined.*
Add flour mixture and mix on low speed until combined, scrape down sides of the bowl as needed, stop when the flour is mixed it but do not overmix.
Gather the dough into a ball and cover with plastic wrap and refrigerate the dough for 15-30 minutes.
Place powdered sugar in a bowl (I used the flour mixture bowl).
Use a tablespoon sized measuring spoon to measure the dough and a regular teaspoon to scrape the dough out into the bowl of powdered sugar.
Use your fingers to roll the dough in the powdered sugar and shape it into a ball.
Place the powdered sugar covered dough on your prepared cookie sheet about 2 inches apart from each other, repeat measuring and rolling the dough
Bake for 12-13 minutes until the cookies are puffy, slightly cracked, and golden brown at the bottom.
Allow the cookies to cool on the tray for a few minutes then transfer to a wire rack to cool completely.