Gather the ingredients. Preheat the oven to 375 F.
Bring a large pot of salted water to boil. Add 8 ounces penne pasta (about 2 cups) and cook for 2 minutes less than indicated in the package directions. Drain well, reserving ½ cup of the pasta cooking water.
While the pasta is cooking, heat 3 tablespoons neutral cooking oil in a 12-inch cast-iron skillet over medium-high. Add 1 small green bell pepper, sliced, 1 small orange bell pepper, sliced, and 1 small red bell pepper, sliced and cook, stirring occasionally, until starting to soften, 2 to 3 minutes.
Add 1 large red onion, sliced to skillet and cook, stirring occasionally, until onions and peppers are softened, about 4 more minutes.
Stir in 2 garlic cloves, finely chopped and cook, stirring constantly, until fragrant, about 30 seconds. Add 3 tablespoons fajita seasoning and 3 cups (about 12 ounces) shredded rotisserie chicken, stirring to combine.
Pour in 1 ½ cups heavy whipping cream and reserved ½ cup pasta water. Bring to a simmer over medium, stirring often. Simmer, stirring often, until the sauce is slightly thickened, 2 to 3 minutes. Remove from the heat.
Stir the cooked pasta and 1 cup (4 ounces) of the pepper Jack into the mixture in the skillet. Sprinkle the remaining 1 cup (4 ounces) pepper Jack evenly over top.
Bake until the cheese is melted, about 5 minutes. Turn the oven to broil and broil until the sauce is bubbling and the top is starting to brown, about 2 minutes. Garnish with chopped fresh cilantro and serve hot.
