In a large skillet, melt the butter over medium-high heat. Stir in the onion and carrot and cook for about 2-3 minutes until onions are translucent. Then add the garlic and salt, stirring often for about 1 minute.
Stir in the flour until combined.
Pour in the chicken broth, being sure to scrape the bottom of the pan.
Then add the pasta, bring to a boil and then simmer, stirring occasionally for about 8-10 minutes, until pasta is al dente.
Add the heavy cream; bring to a boil. Reduce to a simmer.
Add the cooked chicken and peas. Taste and add additional salt and pepper, if needed.
Garnish with parsley and serve.