01 - Bring a large pot of salted water to a boil. Cook the spaghetti until al dente, then drain and set aside.
02 - In a large skillet over medium heat, melt the butter. Add minced garlic and sauté for 1 minute until fragrant. Pour in the heavy cream and milk, then stir in the chopped chipotle peppers and adobo sauce. Simmer the mixture for 2 to 3 minutes, allowing flavors to blend.
03 - Gradually add shredded cheddar cheese to the sauce, stirring constantly until melted and smooth. Stir in the shredded chicken and cook for an additional 2 minutes to heat through.
04 - Add cooked spaghetti to the skillet and toss until the pasta is thoroughly coated in the chipotle cream sauce. Season to taste with salt and freshly ground black pepper.
05 - Transfer to serving plates. Sprinkle with chopped fresh cilantro and serve immediately, offering lime wedges on the side.