Preheat oven to 400 degrees.
Cook the spaghetti, drain and toss with a tablespoon of olive oil.
While the spaghetti is cooking, heat 1 tablespoon butter in a skillet.
Add the onion, diced red bell pepper and cubed chicken breasts and cook for about 4 minutes over medium high heat, stirring often until the chicken is lightly browned. Remove from the pan and set aside.
Melt 3 tablespoons of butter in the skillet. Whisk in flour, salt and pepper. Cook for 30 second to 60 seconds. Whisk in chicken broth, Greek yogurt and heavy cream until smooth. Stir in 1 cup of the shredded cheese
Stir in the spaghetti, chicken and peppers. If you are not using an oven-proof skillet, transfer the tetrazzini to a large baking dish or 9x13 inch pan.
Top with 1 cup of shredded cheese.
Bake at 400 degrees for 20 minutes or until the cheese is melted and lightly toasted.