Preheat an indoor grill or cast iron skillet to medium
Add the chicken stock and thyme to a heavy bottomed pot set over medium-high heat and bring to a simmer.
In the meantime, remove any excess moisture from the chicken cutlets. Grill or fry the chicken cutlets for about 5-6 minutes on each side until cooked through. Transfer the chicken to a cutting board and loosely tent with aluminum foil.
Add the pasta to the simmering stock and return to a simmer. Cover and cook until the pasta is tender, about 6-8 minutes.
Meanwhile, in a large bowl or 4 cup pourable measuring cup, beat the eggs and lemon juice together.
Once the pasta is cooked, slowly stream about 1 cup of hot stock into the egg and lemon mixture while whisking continually.
Turn the heat to low under the soup. Slowly stream the egg and lemon mixture into the broth and pasta mixture while continually stirring. Stir in half the dill.
Cut the grilled chicken into ½-inch pieces and add to the soup.
