Prepare Zucchini: Grate two medium zucchinis, squeeze out moisture using a kitchen towel, and set aside.

Mix Ingredients: In a bowl, combine squeezed zucchini, 1 cup of cheddar cheese, 1/2 cup of flour, and one beaten egg. Add optional herbs, stir until combined.

Cook Patties: Heat a skillet over medium heat, melt 1-2 tablespoons of butter, form patties with the mixture, and cook until golden brown, about 3-4 minutes per side.

Assemble Sandwiches: Layer two patties with extra cheese, return to skillet and cook until cheese melts, about 2-3 minutes per side.

Serve: Let cool slightly, slice, garnish with fresh herbs, and serve with tomato soup.