1. Preheat the oven to 350°. Line baking sheets with parchment paper.
2. In a medium bowl, whisk together the flour, baking soda, and salt. Whisk in the lemon zest. These are the dry ingredients. Set aside.
3. In a small bowl or measuring cup, stir together the yogurt, milk, and extracts. These are the wet ingredients. Set aside.
4. Combine the butter and sugar in the bowl of a stand mixer. Beat until light and fluffy. Beat in the eggs, one at a time. Scrape down the sides and bottom of the bowl. Beat again until thoroughly mixed.
5. With the mixer on low speed, mix in the zucchini.
6. With the mixer still on low speed, mix the wet and dry ingredients one after another in the following order: 1/3 of the dry, 1/2 of the wet, 1/3 of the dry, rest of the wet, rest of the dry. Mix until just blended.
7. Scrape down the sides and bottom of the bowl and give the mixture a final stir by hand.
8. Scoop the dough by the rounded tablespoonful onto the prepared baking sheets, leaving about 2″ between each.
9. Bake for 10-15 minutes or until the edges are golden and the centers are set (like cake).
10. Transfer the sheets to racks. Cool the cookies on the sheets for one minute. Transfer the cookies, still on the parchment paper, to racks to cool completely.
11. For the Icing: in a medium bowl, combine the powdered sugar and lemon juice. Beat with an electric mixer until smooth.
12. You can use a spoon or piping bag to drizzle the icing over the cookies. Let the icing set.