Zucchini, Rice and Cheese Gratin (Tian de Courgettes au Riz)

Name: Zucchini, Rice and Cheese Gratin (Tian de Courgettes au Riz)
Cuisine: European, Mediterranean, French
Ingredients: Butter for dish; 2 1/2 pounds (about 1 1/8 kg) zucchini; 2 1/2 teaspoons kosher salt (I use Diamond brand, use 1 1/2 of other brands); 1/2 cup (90 grams) plain, uncooked white rice; 1 medium onion, minced (about 1 cup); 5 tablespoons (75 ml) olive oil, divided; 2 large cloves garlic, mashed or finely minced; 2 tablespoons (15 grams) all-purpose flour (optional); 1/2 cup milk, as needed, although water or broth of your choice would work just fine [1/2 cup needed for streamlined directions, less for original]; 2/3 cup (55 grams) grated Parmesan cheese, divided; Salt and pepper