Pat chicken dry and place in a medium bowl. In a separate small bowl, whisk together all fajita seasoning spices. Toss the chicken with about two-thirds of the seasoning blend.
Heat olive oil in a large, deep skillet over medium-high heat until shimmering. Add chicken in a single layer and sear for 3-4 minutes per side until a deep golden-brown crust forms. The chicken will not be cooked through. Transfer to a clean plate.
In the same pan, add sliced onions and bell peppers. Sauté, stirring occasionally, for 5-7 minutes until softened with charred edges.
Make a well in the center of the veggies and add the minced garlic. Cook for 30-60 seconds until aromatic. Add the remaining third of the fajita seasoning and stir for 30 seconds to toast the spices. Transfer veggies to the plate with the chicken.
Pour the chicken broth into the empty skillet, scraping up all the browned bits from the bottom of the pan as it comes to a simmer.
Bring broth to a full simmer, then stir in the uncooked penne. Reduce heat to maintain a lively simmer. Cook, stirring frequently, until pasta is just al dente (check your package instructions, and start tasting 2 minutes before the time is up). Most of the broth will be absorbed.
Turn the heat down to LOW. Pour in the heavy cream and stir gently to combine.
Turn the heat OFF completely. Immediately add the shredded cheese, stirring constantly until it melts into a smooth, velvety sauce.
Return the chicken, veggies, and any accumulated juices to the skillet. Stir until everything is coated and warmed through.
Finish by stirring in the fresh lime juice and chopped cilantro. Serve immediately.