Slice off half the eggplant skin and slice the eggplant into 1/2-inch thick discs. Then stack the discs and cut the eggplant into 1/2-inch-wide batons. Salt the eggplant and let it drain on a kitchen towel for 20 minutes.
Place the mint and 1 cup of the basil leaves with the toasted pine nuts in the bowl of a food processor. Season with salt and pepper and grate in 1 clove garlic. Add in the lemon zest and juice, then turn the processor on and stream in about 1/4 cup olive oil. Place the pesto in a large shallow bowl that you can serve the zucchini pasta from. Stir in the cheese.
Using a vegetable peeler and shaving the length of the zucchinis very thinly slice them into wide, pasta-like ribbons. If the zucchini are large and seedy, discard the seeds once you get to the center. Flip the zucchini over and peel until you reach seeds. If the zucchini are firm and small to medium in size you'll be able to use all of the vegetable.
Place the vegetable stock and 2 cups water in deep skillet.
Heat the remaining 3 tablespoons olive oil, 3 turns of the pan, in a large skillet and heat over medium-high heat. Add the eggplant to the hot oil and lightly brown, 6 to 7 minutes, tossing occasionally. Toss and combine with the chile flakes and remaining garlic. Add the tomatoes and cover the pan with a tight fitting lid. Shake the pan occasionally and cook until the tomatoes burst, 7 to 8 minutes more.
Meanwhile, heat the stock and water to low rolling boil, add the zucchini, cook 2 minutes. Use a spider or tongs to remove the zucchini to the pesto. Add 1 cup cooking liquids and toss to coat and combine, using additional cooking liquids if necessary. Top with extra cheese to serve.
Remove the lid from the eggplant and tear in the remaining 1/2 cup basil leaves. Toss to combine.
Serve the zucchini piled up on plate with the eggplant alongside, topping eggplant with crumbled ricotta salata.