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1
Position a shelf at the lowest position in the oven and preheat to 450 degrees F.
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2
Cut the backbone out the chickens with kitchen scissors and reserve for another use or discard.
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3
In a shallow dish combine the thyme, 9 cloves crushed garlic, lemon juice and 1/3 cup of extra-virgin olive oil.
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4
Add the chickens and coat thoroughly in the mixture, cover and marinate in the refrigerator for up to 1 hour.
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5
Remove the chicken from the marinade, discard marinade.
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6
Turn the birds breast-side up and fold the wing tips back and under.
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7
Season both sides with some salt and pepper and the paprika.
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8
Place the chickens bone-side up on a broiler pan and position the legs in the center.
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9
Roast in the oven until the chickens are 3/4 cooked (about 140 to 150), about 25 to 30 minutes.
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10
Put the whole grape tomatoes, scallions, garlic cloves, and basil leaves in a large bowl, drizzle with 1 tablespoon of the olive oil and sprinkle with salt and pepper to taste.
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11
Turn the vegetables until they are lightly coated.
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12
After the chickens have cooked for about 25 minutes, arrange the vegetables around them.
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13
Turn the oven to broil and broil until the vegetables are charred, about 10 to 15 minutes.
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14
An instant-read thermometer should reach 170 degrees F. Transfer the chicken and vegetables to a cutting board.
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15
Pour off all except about 2 tablespoons of chicken fat from the pan and set aside.
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16
Meanwhile, bring a large pot of cold water to a boil and salt it generously.
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17
Add the spaghetti, and cook, stirring occasionally, until al dente, 8 to 10 minutes.
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18
Drain, reserving 1/2 to 3/4 cup of the pasta water and transfer the both to a serving bowl.
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19
Squeeze the garlic cloves from their skins, and chop them up with the scallions, once chopped transfer to a bowl and add the charred grape tomatoes, stir to make a chunky relish.
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20
Once the chicken is cooked and resting, place the pan you broiled the chicken in on the cook top over medium heat.
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21
Add the red wine vinegar, Worcestershire sauce and the reserved pasta cooking water, bring up to a simmer scraping the bottom of the pan with a wooden spoon.
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22
Add the cooked spaghetti and chopped parsley, stir to coat and continue to cook for 1 minute.
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23
Transfer the spaghetti to a serving bowl.
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24
Carve the chicken, top with some of the chunky relish and serve with some of the spaghetti on the side.
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25
Garnish with grated Parmesan, if using.