Preheat the oven to 350F and grease a 24-count mini muffin pan. See the note below regarding cooking time if using a regular muffin pan.
If using, trim both ends of the green onions and finely chop. Separate the green end from the white. Or, finely chop the shallot.
In a medium skillet, heat oil over medium heat. Add the zucchini, carrots, and green onions or shallot, and cook, stirring, for 5-7 minutes until the veggies begin to soften. Remove from heat and set aside to cool down to room temperature.
In a large bowl, combine veggies, eggs, grated cheese, and salt. Spoon mixture into mini muffin pan.
Bake for 15-18 minutes. Allow veggie egg bites to cool in the pan before carefully removing with a small knife or spatula.
Once cooled, refrigerate the egg bites in an airtight container or zip bag for up to 3 days.
For snack box:
To enjoy these at room temperature, place 4 to 6 egg bites inside the main compartment of a lunch container.
To eat warm, heat the veggie egg bites in the microwave for 1 minute, stopping the microwave half way through to flip them over. Immediately transfer them inside a thermos container and close the lid.
Finish packing this meal by adding fruit, veggies, and any other sides inside a bento box. Pack everything inside a lunch bag.
Notes
The cooking time using a mini muffin tray (yields 24) is approximately 16 to 18 minutes. Using a regular-sized muffin tray (yields 12) requires a longer baking time of approximately 26 to 28 minutes.