Roasted Eggplant and Sautéed Greens Lasagna

Name: Roasted Eggplant and Sautéed Greens Lasagna
Ingredients: 2 to 3 small-ish eggplant (about 2 to 3 pounds); grapeseed oil; kosher salt; 10 to 12 ounces greens, such as Swiss chard, kale, or mustard greens, leaves removed from stems and roughly chopped (you should have about 8 oz. greens post trimming); 1 quart tomato sauce, homemade is best, see notes above; 1 box no-boil noodles (about 9 oz, you'll need 12 sheets, see notes above); 4 ounces Parmigiano Reggiano, grated (about 1 cup); 8 ounces fresh mozzarella (not stored in brine), pulled into small pieces (about 1 cup)