Preheat the oven to 375°F (190°C), line a 12-cup muffin pan, and squeeze the grated zucchini thoroughly to remove as much excess liquid as possible.
In a large bowl, whisk together the flour, baking powder, garlic powder, and salt until the dry ingredients are evenly distributed.
In a separate bowl, whisk the eggs, milk, and olive oil until smooth, then stir in the drained zucchini and chopped chives.
Pour the wet ingredients into the flour mixture and fold gently with a spatula until only a few dry streaks remain.
Add the shredded cheddar and fold just until incorporated, taking care not to overmix because that can make the muffins dense.
Divide the batter evenly among the muffin cups and bake for 20–22 minutes until the tops are lightly golden and spring back when touched.
Cool for about 5 minutes in the pan before transferring the muffins to a rack, then serve warm or refrigerate for later.