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Preheat the oven to 400 degrees. Toss peppers, onion and garlic with 1 tablespoon olive oil. Spread evenly on a baking sheet, sprinkle with salt and roast until the onion is soft and translucent, about 20-25 minutes, stirring once halfway through.
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While the vegetables are roasting, boil the pasta until al dente in a pot of salted water. Drain the pasta and reserve 1/2 cup of the pasta cooking water. Set aside.
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Add 1 tablespoon olive oil to a skillet over medium heat. Add the broccoli and yellow peppers and cook until they are fork tender, about 5-7 minutes. You can add a small splash or two of water to the skillet to help the cooking along. Season vegetables with salt and pepper and remove from heat.
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When the vegetables are done roasting, remove them from the oven and let cool slightly, then peel peppers and remove the seeds.
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Add peppers, onion and garlic to a high speed blender. Drain the soaked cashews and add to blender along with 1 tablespoon olive oil, basil, nutritional yeast, 1/2 teaspoon sea salt. Blend until smooth and creamy, adding reserved pasta water one tablespoon at a time to thin the texture (I used 5 tablespoons) and scraping down the sides of the blender a few times. Blending can take about 1-2 minutes to get the sauce to a velvety smooth consistency.