Preheat oven to 350°F and line two baking sheets with parchment paper, set aside.
Grate zucchini and carrot and place in a fine mesh strainer, over a bowl. Sprinkle with ¼ tsp salt and mix around. Allow to sit for 10-15 minutes, and liquid will drain out from the zucchini.
After 15 minutes, taking a handful of the zucchini mixture at a time, squeeze out any excess liquid (there will be a lot), discard the liquid and place the zucchini in a dry bowl. Repeat with remaining zucchini.
Add all ingredients into the bowl with the drained and mix until combined. Form into patties (about 2 tbsp) and place onto prepared baking sheets.
Bake in preheated oven for 20-25 minutes, flipping halfway through. They will be lightly browned.
Allow to cool and store in an airtight container in the fridge for up to 4 days. These freeze very well too, so make a double batch if you have a ton of zucchini!