Scoop out the interior of the zucchini quarters with a small spoon.
Using 1 Tbsp of salt, salt the cut sides of the zucchini and place cut side down. Set aside while you continue with the recipe.
Heat a large skillet over medium heat.
When hot, add 1 Tbsp olive oil, garlic and oregano and cook, stirring, for one minute.
Add ground beef and cook, stirring only occasionally, for 5-7 minutes under nicely browned and no longer pink. Salt with 1-2 teaspoons of salt. Taste it and see how much you want.
Add tomato sauce, mix together, and cook for 5 minutes more. Remove from heat.
Pat zucchini quarters dry with a paper towel on all sides. The salt will have drawn out some of the moisture. Rub the zucchini all over with the remaining 2 Tbsp of olive oil.
Fill each zucchini boat with a few tablespoons of the meat mixture and place on large, lined baking sheets.. Be generous.
Top with mozzarella and parmesan cheese.
Cover the baking sheets with tin foil and bake for 30-40 minutes until the zucchini is soft and stuffing is bubbling.
Remove the tin foil cover, turn the oven to broil, and broil for 5 minutes to brown the cheese.
Remove from oven, top with fresh basil, and allow zucchini to sit for 10 minutes before serving.