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1
Combine chicken breasts and chicken broth in a saucepan over medium-high heat. Bring to a boil, cover, and reduce heat to low; simmer for 5 minutes. Turn breasts, cover, and simmer another 5 minutes. Remove from heat and let sit with the cover on for 15 minutes.
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2
Remove chicken breasts from the broth and set aside to cool, reserving the broth in the saucepan. Once the chicken is cool enough to handle, cut into bite-size slices.
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3
Return the chicken broth to medium heat and cook until reduced to 1 cup.
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4
Stir garlic, black pepper, and heavy cream into the reduced broth; bring to a simmer and remove from heat.
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5
Whisk egg yolks in a bowl until smooth. Beat 1 tablespoon of the warm cream mixture into the eggs until thoroughly incorporated; repeat until about 1/2 cup of the warm cream mixture is used.
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6
Whisk the warm cream and egg mixture back into the saucepan with the remaining cream mixture. Cook over medium-low heat, whisking constantly, until the mixture almost comes to a simmer and thickens, about 5 minutes. Season with salt and black pepper to taste.
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7
Bring a large pot of lightly salted water to a boil. Cook fettuccine in boiling water, stirring occasionally, until nearly cooked through, about 7 minutes. Drain.
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8
Stir parsley, 1 cup of Parmigiano-Reggiano, and cream mixture into the pasta. Remove from heat, cover, and let sit for a few minutes until thick.
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9
Fold chicken and 1 cup Parmigiano-Reggiano into the pasta mixture to serve.
