Heat olive oil in a large skillet over medium-high heat.
In a medium bowl, combine chicken pieces with cumin, chili powder, smoked paprika, garlic powder, salt, and black pepper. Toss to coat evenly.
Add the seasoned chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove chicken from the skillet and set aside.
In the same skillet, add diced onion and bell peppers. Cook for 4-5 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Pour in the diced tomatoes with their juice and chicken broth. Stir to combine.
Add the uncooked penne pasta and frozen corn kernels to the skillet. Stir well.
Bring the mixture to a boil, then reduce heat to medium-low. Cover and simmer for 12-15 minutes, stirring occasionally, until the pasta is tender and most of the liquid is absorbed.
Return the cooked chicken to the skillet and stir to combine.
Sprinkle shredded cheddar cheese over the top. Cover the skillet and cook for an additional 2-3 minutes until the cheese is melted.
Remove from heat and stir in chopped cilantro.
Serve immediately with lime wedges on the side for squeezing over the dish.