Bring a large pot of salted water to a boil. Add the pasta and cook according to the package directions for al dente. Drain the pasta and set aside.

In a medium bowl, toss the chicken with 1 tablespoon of fajita seasoning and 1/2 teaspoon of salt.

In a large Dutch oven, heat 1 tablespoon each of butter and olive oil over high heat. Add half of the chicken in a single layer. Cook until deep golden, 2 to 3 minutes, then stir and cook until golden on the other side, 1 to 2 more minutes. Remove to a plate with a slotted spoon.

Add the remaining chicken and repeat. Add the remaining 1 tablespoon each of butter and olive oil to the drippings in the pot. Add the garlic, bell pepper, poblano, red onion, mushrooms, and the remaining 1 teaspoon of salt. Cook, tossing occasionally, until the vegetables are crisp-tender, 3 to 4 minutes. Remove the vegetables to a plate.

Add the chicken broth to the pot and scrape up any browned bits from the bottom with a wooden spoon. Bring to a simmer and cook for a couple of minutes until slightly reduced.

Reduce the heat to medium. Stir in the heavy cream, adobo sauce, and the remaining 1 tablespoon fajita seasoning. Cook, stirring occasionally, until thickened, 5 to 6 minutes. Season with salt and pepper as needed.

Return the chicken and vegetables to the pot. Add the pasta and cook, tossing, until coated and heated through, 2 to 3 minutes. Serve topped with cilantro.