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1
Place summer squash in a wire mesh strainer set over a bowl; place eggplant in a second wire mesh strainer and set over a second bowl. Toss both with a liberal amount of kosher salt and let stand to drain at least 15 minutes and up to 1 hour. Discard any liquid that collects in the bowls.
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2
In a large skillet, heat 3 tablespoons olive oil over medium-high heat until shimmering. Add onion and garlic, season with salt, and cook, stirring, until softened, about 6 minutes. Scrape onion and garlic onto a rimmed baking sheet and spread in an even layer to cool for 3 minutes. Transfer onion and garlic to a large pot.
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3
Meanwhile, add 3 more tablespoons olive oil to skillet and heat over medium-high heat until shimmering. Add bell pepper, season with salt, and cook, stirring, until softened, about 7 minutes. Scrape bell pepper onto the rimmed baking sheet in an even layer to cool for 3 minutes. Transfer bell pepper to pot with onion.
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4
Add 3 more tablespoons olive oil to skillet and heat over medium-high heat until shimmering. Add summer squash and cook, stirring, until softened, about 4 minutes. Scrape onto rimmed baking sheet in an even layer to cool for 3 minutes. Transfer to pot with onion and bell pepper.
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5
Add remaining 3 tablespoons olive oil to skillet and heat over medium-high heat until shimmering. Add eggplant and cook, stirring, until softened, about 4 minutes; add more olive oil as needed if skillet dries out while cooking eggplant. Scrape eggplant into pot with other vegetables and stir to combine.
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6
Set pot of vegetables over medium-high heat and stir in tomato puree and herb bundle; heat until ratatouille is gently bubbling, then lower heat to medium and cook, stirring, until tomato puree coats vegetables in a thick sauce, about 15 minutes. Discard herb bundle. Season with salt, stir in chopped parsley (if using), and drizzle with a small amount of fresh extra-virgin olive oil. Serve right away, or chill and serve either reheated, slightly chilled, or at room temperature.