In a large skillet or pot with a lid, melt the unsalted butter over medium-high heat. Add the minced onion, celery, and carrots, then stir into the butter. Cook for about 5 minutes, stirring occasionally, until the vegetables are softened.
Add the cubed chicken thighs, freshly ground black pepper, and kosher salt, then stir to combine everything. Continue cooking, stirring occasionally for 7 to 10 minutes, until the chicken is cooked and no longer pink.
Add the white wine to deglaze the pot and allow it to cook for 2 to 3 minutes so the wine reduces slightly. Then, stir in the all-purpose flour and freshly minced rosemary.
Then, add the low-sodium chicken broth, increase the heat to high, and bring to a simmer. Add the uncooked egg noodles, bring back up to a simmer, place the lid on the pot, and reduce the temperature to medium-low. Cook for 15 minutes, stirring every five minutes.
Stir in the frozen peas, replace the lid, and cook for an additional 5 minutes.
Top with sprigs of fresh rosemary and serve immediately.