In a large bowl, combine the flour, cheese, salt, baking powder and baking soda.
In another bowl, whisk the eggs, milk, sugar and both butters.
Stir into dry ingredients just until moistened. Fold in zucchini and onion.
Pour into a greased mini loaf pan or 9"x5" loaf pan.
Bake at 350° until a toothpick inserted in the center comes out clean, about 45 minutes for mini loaves or 1 hour for a 9"x5" loaf.
Cool for 10 minutes before removing from pan to a wire rack. Cut into 12 equal pieces.