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1
In a saucepan, bring chicken stock to a boil.
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2
Meanwhile, cut the chicken breasts into lengthwise strips about the width of a finger; drop the strips into the boiling stock.
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3
Cover and bring to a boil; decrease heat and simmer for 4 minutes.
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4
Remove the cover and set aside, allowing the chicken to cool in the liquid.
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5
When cool, transfer chicken to a cutting board and reheat the stock.
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6
Meanwhile, melt 1 tablespoon of the butter in another large saucepan.
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7
Stir in the garlic and cook over low heat until the garlic becomes golden.
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8
Add 1 cup water to prevent the garlic from browning; stir to combine.
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9
Add in carrots and salt; cook over moderate heat, stirring frequently, until the mixture is nearly dry with just a bit of water left.
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10
Be vigilant and stir constantly toward the end of this step to be sure the carrots do not brown at all.
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11
Add the hot stock and tomato juice; cover and bring to a boil; decrease heat, set the cover ajar, and simmer gently for 35 minutes or until the carrots are very soft.
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12
Puree with an immersion blender until you have a smooth puree; set aside.
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13
Cut the chicken strips lengthwise into 1/8-inch thick slices, then cut across to make 1/8 inch dice; add the chicken to the sauce and reheat gently.
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14
Bring a large pot of water to a boil; generously salt the water and add in the fettuccine.
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15
Cook, stirring often, until al dente; drain the pasta and transfer to a heated platter or shallow gratin dish.
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16
Toss with the remaining butter and fold enough sauce to coat the noodles generously.
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17
Sprinkle with Parmigiano-Reggiano; serve immediately; pass more cheese at the table.