Step 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.
Step 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.
Step 3
Return the chicken broth to medium heat and cook until reduced to 1 cup.
Step 4
Stir garlic black pepper and heavy cream into the reduced broth; bring to a simmer and remove from heat.
Step 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.
Step 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.
Step 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.
Step 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.
Step 9
Fold chicken and 1 cup Parmigiano-Reggiano into the pasta mixture to serve.