Place the oil in a large saute pan on medium high heat. Add the chopped onions, celery, carrots, thyme, and salt, then saute for 6 minutes to soften. Stir occasionally.
Add the broth and bring to a boil. Stir in the pasta. Cover the pan and simmer for 8 minutes.
Meanwhile, chop the turkey breast into 1-inch square pieces, and defrost the frozen peas in a colander under warm water.
Stir in the peas, shredded cheese, and milk, and allow it to simmer for 2 minutes.