Preheat your oven to 200°C (390°F). Line a baking sheet with parchment or a silicone mat to prevent sticking.
Using a grater, shred the carrots and zucchini into a mixing bowl. Squeeze out as much excess moisture as possible using a clean kitchen towel or paper towels. This helps keep the bites crispy.
Add the breadcrumbs, shredded cheese, beaten egg, chopped herbs, salt, and pepper to the shredded vegetables. Mix everything thoroughly until the mixture is cohesive and easy to shape.
Using a spoon or your hands, shape the mixture into small, flat bites about 1.5 inches wide. Place each shaped bite evenly spaced on your prepared baking sheet.
Lightly brush or spray the bites with olive oil to help them crisp up in the oven. Bake for 15-20 minutes, or until golden brown around the edges and firm to the touch.
Once baked, remove the veggie bites from the oven and let them rest for about 5 minutes. They will firm up slightly as they cool, making them easier to handle.
Serve the bites warm or at room temperature, garnished with fresh herbs if desired. They make a satisfying snack with a crispy exterior and tender interior.