How to Make It
Slice the eggplant in half lengthwise, and with a paring knife, score the flesh in a diamond crosshatch pattern. Squeeze the eggplant to open the cuts and sprinkle the top and insides with salt. Set aside for 30 minutes.
Preheat the oven to 400º. Prepare a baking sheet with a nonstick baking mat or parchment paper and set aside. In a medium pot over high heat, bring the quinoa, water and 1/2 teaspoon kosher salt to a rolling boil, stirring occasionally. Reduce the heat to low, and simmer until the quinoa has fully absorbed the water, about 15 minutes. Remove from the heat and set aside.
After the eggplant has rested for 30 minutes, gently squeeze the edges to release the juice, and wipe the surfaces dry with a paper towel. Arrange, fleshy side up, on the baking sheet, and brush each half with olive oil (about 1 tablespoon total). Roast until the top of the eggplant begins to brown and crisp, about 1 hour. Let the eggplant cool for at least 10 minutes, then using a tablespoon, scoop all of the flesh of the eggplant into a large serving bowl. Add 1 tablespoon olive oil, the Parmigiano-Reggiano cheese, and the cooked quinoa. Toss gently, salt and pepper to taste, sprinkle with red chili flakes to taste, and serve.