Preheat your oven to 200°C (390°F) and line a baking sheet with parchment paper or a silicone mat. Gather your shredded vegetables, cheese, breadcrumbs, and spices.
Finely shred the carrots and zucchini, then use a clean kitchen towel to squeeze out as much excess moisture from the zucchini as possible. This helps the bites stay crispy.
In a large mixing bowl, combine the shredded vegetables, grated cheddar, toasted panko breadcrumbs, smoked paprika, garlic powder, and a splash of olive oil. Mix thoroughly until everything is evenly coated and well incorporated.
Add the beaten egg to the mixture and stir until it binds everything together. If the mixture feels too loose, sprinkle in a little more breadcrumbs until it holds its shape.
Using a tablespoon or cookie scoop, shape the mixture into small, compact rounds or mounds and place them on the prepared baking sheet, spacing them evenly apart.
Bake in the preheated oven for 18-20 minutes, until the edges turn golden brown and the bites feel firm and slightly crispy around the edges.
For extra crispiness, switch to the broiler setting for 1-2 minutes, keeping a close eye to prevent burning. The bites should crackle slightly and look irresistibly golden.
Remove the bites from the oven and let them cool on the baking sheet for 5 minutes. They will firm up as they rest, making them easier to handle and eat.
Serve the baked veggie bites warm or at room temperature, perhaps with a side of sour cream or your favorite dip for added flavor.
