Start by bringing a large pot of salted water to a boil. Add the penne pasta and cook according to the package directions until al dente. Once cooked, drain and set aside.
In a large skillet, heat the olive oil over medium-high heat. Add the diced chicken breast and season with kosher salt and freshly ground black pepper. Cook the chicken for about 5-7 minutes, or until it’s golden brown and cooked through, stirring occasionally.
Once the chicken is fully cooked, add the diced red bell pepper and green beans to the skillet. Sauté for an additional 4-5 minutes, or until the vegetables are tender but still crisp. Add the minced garlic and cook for another minute, stirring constantly.
Reduce the heat to low, and add the cooked penne pasta to the skillet. Stir everything together, ensuring that the pasta is well-coated with the olive oil and mixed with the chicken and vegetables.
Sprinkle the shredded asiago cheese over the pasta mixture. Gently toss everything together, allowing the cheese to melt and create a creamy sauce. If the mixture seems too thick, add a splash of pasta water to loosen it up.
Finally, stir in the freshly minced basil. Taste and adjust the seasoning with more salt and pepper if needed.