Place a large saute pan over medium-high heat. Place the poblano peppers in the dry pan and blister the peppers on all sides, creating large black spots. Use tongs to move the peppers to a large zip bag. Close the bag and let the peppers steam for 10 minutes.
Pour 4 cups chicken broth into the saute pan. Bring to a boil, then stir in the pasta and garlic. Cover and simmer for 5 minutes. Then stir the pasta well to separate.
Meanwhile scrape off the waxy skin from the peppers. Remove the seeds and stems, then chop the peppers into small pieces. Once the pasta is mostly cooked, add the cream cheese and chopped poblanos to the pan. Stir to melt the cheese and incorporate the peppers.
Stir in the chopped turkey and shredded cheddar cheese. Add one more cup of chicken broth to loosen up the sauce. Taste, then salt and pepper as needed. Stir until the turkey is warmed through. Serve immediately.
NOTE: Poblano peppers are usually mild. However, you can end up with a spicy one! At the market wiggle the stems, then smell the top. If a pepper smells spicy select another one. Even one hot poblano can make this dish overpowering.