In a large pot or deep skillet, heat olive oil or butter over medium heat. Once melted, toss in the chopped onion (if using) along with the minced garlic. Sauté until soft and fragrant, about 3-4 minutes.
Add the cooked chicken into the pot, then stir in the finely chopped chipotle peppers along with the adobo sauce.
Pour in the chicken broth and heavy cream, stirring until well combined.
Add uncooked penne pasta, stir to ensure all pieces are submerged, bring to a gentle simmer, cover, and cook for about 10-12 minutes, stirring occasionally.
Once the pasta is tender and most of the liquid has been absorbed, reduce heat to low and stir in the shredded cheddar cheese until melted.
Taste and adjust seasoning with salt, pepper, or extra adobo sauce as desired.
Let the dish sit for about 2-3 minutes before serving to thicken slightly.