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Preheat the oven to 375 degrees F.
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In large pot, cook pasta according to package directions, adding in peas when 1 minute of cooking time remains. Drain and set aside.
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In large oven-proof skillet over medium-high heat, heat olive oil. Add onions, garlic, salt, carrots, broccoli and thyme. Cook, stirring occasionally, 7-8 minutes or until vegetables are soft.
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Turn off skillet. Stir in pasta/peas mixture and tuna until well combined. Set aside.
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In saucepan over low heat, stir together sauce ingredients until well combined and smooth, about 3-4 minutes.
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Pour sauce over pasta mixture and gently stir to combine. Taste and season with salt and pepper.
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Bake for 15 minutes or until sauce is bubbling at the edges.
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To serve, sprinkle with chopped parsley, if desired.