Place the potatoes in a large saucepan or stockpot and add enough water to cover. Add ½ teaspoon of salt to the pot. With the heat on high, bring the water to a boil. Once it reaches a boil, reduce the heat and simmer for about 15 minutes, until the potatoes are tender. Drain the potatoes and then add to a large bowl.
Meanwhile, spread the red onion, green beans, eggplant and zucchini onto a large rimmed baking sheet. Drizzle with the olive oil and toss with the remaining ½ teaspoon salt and the garlic. Bake for 15-20 minutes, stirring once halfway through, until tender. Remove from the oven and add to the bowl with the potatoes.
To make the dressing, add the mustard, lemon juice, vinegar, oregano, salt, pepper and olive oil to a small bowl. Whisk vigorously until smooth. Pour the dressing into the bowl with the potatoes (do this while the potatoes are still hot) and toss to combine. Once the potatoes are no longer piping hot, sprinkle on the fresh parsley and basil.
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