Bring a large pot of salted water to a boil. Meanwhile, melt the butter in a large skillet over medium-high heat. Add the shallot and cook until slightly softened, about 1 minute. Add the celery, carrots, thyme, 3/4 teaspoon salt and a few grinds of pepper and cook until the vegetables soften, about 2 minutes. Add the sherry and cook until slightly reduced, about 2 minutes. Stir in the heavy cream and nutmeg and bring to a boil. Reduce the heat to medium low and simmer until the sauce thickens slightly, about 5 minutes.
Add the chicken to the sauce; increase the heat to medium and simmer until just cooked through, about 3 minutes. Add the gruyere and parmesan and continue simmering, stirring occasionally, until the cheese melts and the sauce thickens, about 2 minutes (do not boil). Add the parsley; season with salt and pepper.
Add the pasta to the boiling water and cook as the label directs. Drain, then add to the sauce and toss. Sprinkle in the peas; serve topped with celery leaves.