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Preheat the oven to 375 degrees F. Line a medium baking sheet with foil.
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Add tomatoes to the prepared baking sheet. Toss with 1/4 cup olive oil, salt and pepper. Flip all tomatoes to cut side up. Roast tomatoes for 45-50 minutes until golden but not dark. Once roasted keep off to the side for later.
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While the tomatoes roast, bring a large pot of water to a boil. Once boiling, salt the water heavily. Crack the capellini noodles in half and add to pot. Cook according to the packages instructions. Drain and set off to the side.
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Use a vegetable peeler to shave the asparagus stalks. Do about six shavings per side of the asparagus. Then crack off the tops of the asparagus and add it to a large bowl.
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Add the roasted tomatoes and their cooking oil along with the noodles to the large bowl. Toss noodles together with lemon juice, lemon zest, remaining olive oil, salt, pepper, and fresh basil. Taste and add more salt or pepper accordingly.