Prepare the muffin tin. Place a rack in the middle of the oven and preheat to 400°F/205°C. Spray a regular size muffin tray with nonstick baking spray or line each cup with a muffin liner.
Mix the dry ingredients. In a large bowl whisk together 1 cup (114g) cake flour, 1 cup (120g) whole wheat (or all-purpose) flour, ⅔ cup (135g) sugar, 2 tsp lemon zest, ½ tsp baking powder, ¼ tsp baking soda, and ¼ tsp Kosher salt.
Mix the wet ingredients. In a separate small bowl, whisk together 8 Tbsp (114g) cooled butter, ¾ cup (180g) Greek yogurt, 2 large eggs (100g), 4 Tbsp (60ml) fresh lemon juice, and 1 tsp vanilla extract.
Combine wet and dry ingredients. Pour wet ingredients into dry ingredients and, using a spatula or wooden spoon, mix until just combined. Mixture will be thick. Add in 2 Tbsp (18g) poppy seeds and give one final mix to incorporate.
Bake the lemon poppyseed muffins. Use a large cookie scoop or a ¼ measuring cup to evenly divide batter into muffin liners, filling almost completely to the top. Bake 16-18 minutes, or until a cake tester or knife inserted into the center of the muffin comes out clean. Let cool for 5 minutes, then drizzle with lemon icing.
Make the lemon icing. Place 1 cup (115g) confectioners' sugar in a medium bowl, then add 2 Tbsp fresh lemon juice and 1 tsp vanilla extract. Whisk until smooth. If icing is too thick to drizzle, add the last tablespoon of lemon juice and up to 1 Tbsp (15ml) of milk, as needed, to reach desired consistency. Drizzle over slightly cooled muffins, then enjoy immediately.