Preheat oven to 350°F. Line a 12-cup muffin tin with paper liners or lightly grease with nonstick spray.
Shred zucchini using a box grater. Lightly squeeze out excess moisture with a clean kitchen towel or paper towels. You don’t need to remove all the moisture—just enough so the muffins don’t become soggy.
In a large bowl, whisk together flour, whole wheat flour, baking powder, baking soda, salt, lemon zest, and fresh thyme.
In a separate bowl, whisk together eggs, Greek yogurt, oil, honey or maple syrup, milk, lemon juice, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently stir until just combined. Fold in the shredded zucchini. Be careful not to overmix.
Divide the batter evenly among the muffin cups, filling each about ¾ full. Sprinkle with coarse sugar if desired.
Bake for 18–22 minutes, or until the tops spring back lightly and a toothpick inserted into the center comes out clean. Let muffins cool in the pan for 5 minutes, then transfer to a wire rack.
In a small bowl, whisk together powdered sugar, lemon juice, and lemon zest until smooth. Add more lemon juice for a thinner glaze or more powdered sugar for a thicker drizzle.
Drizzle glaze over cooled muffins and top with extra lemon zest. Let the glaze set slightly before serving.