Preheat oven to 375 degrees.  Shred zucchini on the large holes of box grater.  Transfer to a colander and toss with 1 teaspoon salt.  Allow zucchini to sit for about ten minutes and then transfer it to a clean cotton kitchen towel and squeeze out as much moisture as possible.  Set aside. 

In a large bowl, lightly beat the eggs.  Add zucchini and remaining ingredients except oil.  Combine thoroughly.

Using a large ice cream scoop or a metal measuring cup, transfer a ¼ cup portion of the mixture to a baking sheet.  Press down and shape gently to create a cake that is about ¾ inch thick and 3 inches wide. Repeat with remaining mixture.  Cover with plastic wrap and chill for at least 30 minutes or up to a day. You should have about 12 cakes.

While cakes are chilling, make the Roasted Cherry Tomatoes.  Combine all ingredients except vinegar and basil in a 9 x13 baking dish.  Stir to combine. Transfer to the oven and roast until tomatoes are soft and beginning to burst, about 25 minutes.  Remove from oven and add vinegar and basil. 

Add 3 tablespoons extra-virgin olive oil to a large nonstick skillet.  Heat over medium heat until just shimmering. Using a thin spatula to help you, carefully add 6 cakes to the skillet (they may be a little fragile).  Cook until golden brown on the first side, about 3-4 minutes. Flip each cake over and continue to cook until golden brown on the opposite side and cooked through, about 3 more minutes.  Transfer to a paper towel-lined plate to drain. Sprinkle with additional coarse salt. Carefully wipe out the skillet with a paper towel and add remaining 3 tablespoons of olive oil. Repeat with remaining cakes.  Serve with Roasted Cherry Tomatoes and a generous dollop of ricotta cheese.