Melt 2 tablespoons butter with 1 tablespoon olive oil in a large Dutch oven over medium-high heat.
Add 2 cups onion, 1 cup carrots, 1 cup celery and 1¾ teaspoons salt and cook, stirring often, until vegetables are slightly softened, 6 to 8 minutes.
Add 3 tablespoons flour and stir to coat.
Stir in 4 cups stock and 2 cups milk and let the mixture come to a boil.
Add 4 ounces uncooked noodles to the boiling mixture.
Cover and cook until noodles are al dente, about 8 minutes.
Stir in 3 cups chicken and 1 cup peas and cook until pasta reaches desired doneness and chicken and peas are warmed through, about 1 to 2 more minutes.
Serve immediately.
