Prep: Preheat oven to 350°F and prepare a cookie sheet by lining with parchment or coating with cooking spray. The cookies spread out quite a bit so it may be necessary to use more than one baking sheet or bake in batches.
Wet Ingredients: In a medium bowl, whisk together eggs, oil, and vanilla and lemon extracts, and lemon zest until fully combined.
Combine: Add cake mix and poppy seeds to liquid ingredients and stir with a spatula or spoon to form a smooth dough.
Portion: Form round balls using 2 rounded tablespoons of dough and place 3-4 inches apart on the cookie sheet.
Bake: Bake for 13-15 minutes, rotating halfway through. Cookies will be done when they are almost fully set on the edges and slightly golden on the bottom.
Glaze: While the cookies are baking, whisk together all ingredients until fully combined and no lumps remain. Adjust consistency as needed with milk or powdered sugar. Cover and set aside.
Store: Let cool for a couple of minutes on the cookie sheet before transferring to a wire rack to let cool completely. Once fully cooled, drizzle with glaze and let harden. Store in an airtight container in the fridge for 3-4 days or in the freezer for up to 3 months. Excess glaze can also be stored in the fridge, covered, for 3-4 days.
Freeze for Later: The cookies can be frozen before or after they are baked and kept in the freezer for up to 3 months. Store in an airtight container or ziploc bag. If they have been baked, make sure they are fully cooled first.
Prepare from Frozen: Bake frozen cookie dough according to the recipe instructions - baking times will still be the same. For baked cookies, let thaw to room temperature and enjoy.