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Preheat oven to 400 degrees.
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Slice the tomatoes in half length-wise and then slice into 1/4" half-moons. Arrange in a single layer on a foil-lined baking sheet. Place the chicken breast on the sheet too, and drizzle everything with olive oil and then generously salt and pepper. Roast for about 30 minutes, or until the tomatoes are beginning to turn brown around the edges (you may need to remove your chicken earlier, depending on how thick it is). Set aside.
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While those roast, warm 2 tablespoons of olive oil over medium-low heat in a large skillet, then add onions and stir to coat. Cook until very soft and golden-brown (about 20 minutes), stirring frequently. Put them in a bowl and set aside.
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While your onions are caramelizing, bring water to a boil in a saucepan and cook your noodles to al dente. Drain and set aside.
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After you've taken your onions out of the skillet, add the broth and apple juice, scraping the bottom of the pan to get any browned bits off. Stir in the cream and bring to a simmer, letting it cook for about 10 minutes. Add the Parmesan cheese, garlic and basil, cooking 1 minute more.
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Shred the chicken, then add it, the tomatoes, the noodles, and onions to the cream sauce and stir to coat well. Salt and pepper to taste, and serve immediately.