Place grated zucchini in a colander, toss with 1/2 tsp salt, and let sit for 10 minutes.

Transfer zucchini into a clean kitchen towel or cheesecloth and squeeze out all excess liquid over the sink until completely dry.

In a bowl, combine beaten eggs, garlic, grated cheese, flour, fresh herbs, remaining 1/4 tsp salt, and black pepper. Fold in squeezed zucchini until evenly coated.

Heat 2 tbsp olive oil in a 10-inch skillet over medium-high heat. Add zucchini mixture and press evenly into a flat disk. Lower heat to medium and cook for 6–8 minutes until golden brown underneath.

Slide galette onto a flat plate. Invert skillet over plate, flip together safely, add remaining 1 tbsp olive oil to pan edges, and slide galette back in.

Cook second side for 5–6 minutes until crisp. Slice into wedges and serve hot.