Bring a large pot of lightly salted water to a boil. Place pasta in the pot, cook 8 to 10 minutes, until al dente, and drain.
Melt the butter in a large frypan over medium heat. Stir in the eschallots, red capsicum, yellow capsicum and garlic. Cook 5 minutes, until tender but crisp. Remove vegetables from frypan and set aside.
Place the chicken in the frypan. Season with tarragon, salt and pepper. Cook 10 minutes or until juices run clear.
Return the vegetables to the frypan with the chicken. Mix in the milk, Cheddar cheese and Parmesan cheese. Continue cooking 5 minutes until cheese is melted. Serve over the cooked noodles.