Season cubed chicken with kosher salt and black pepper. Heat olive oil in a large Dutch oven or heavy pot over medium-high heat until shimmering. Add chicken and cook for 5-7 minutes, stirring occasionally, until golden brown and cooked through. Remove chicken with a slotted spoon and set aside.
Add onion, carrots, and celery to the same pot. Cook for 5-6 minutes, stirring occasionally, until vegetables begin to soften and onions become translucent. Add minced garlic and cook for 1 minute until fragrant.
Sprinkle flour over vegetables and stir constantly for 1 minute to cook off the raw flour taste. Gradually pour in chicken broth while whisking continuously to prevent lumps. Add milk, dried thyme, and bring to a gentle simmer.
Cook egg noodles according to package directions in a separate pot of salted boiling water until al dente. Drain well and set aside.
Return cooked chicken to the pot along with frozen peas. Simmer for 3-4 minutes until sauce has thickened enough to coat the back of a spoon and peas are heated through.
Add drained egg noodles to the pot and toss gently to coat completely in the creamy chicken mixture. Stir in fresh parsley and adjust seasoning with additional salt and pepper if needed. Serve immediately while hot.