Bring a large pot of salted water to a boil and cook the penne according to package directions; drain and set aside.
Heat a splash of olive oil in a large high-sided skillet over medium-high heat.
Add the diced chicken to the hot skillet and season generously with kosher salt and freshly ground black pepper; cook, stirring and flipping frequently, until the pieces are browned and about halfway cooked, about 5 minutes.
Stir in the minced garlic and cook for about 1 minute until fragrant, stirring nearly constantly to avoid burning.
Add the butter and lemon juice to the skillet and stir nearly continuously until the butter melts and the chicken is cooked through, about 5 more minutes.
Add the cooked pasta to the skillet and toss well to coat the pasta evenly with the lemon-butter sauce and chicken.
Stir in the finely minced parsley, then sprinkle the freshly shaved Parmesan over the pasta and either toss to combine or leave on top as desired.
Taste and adjust seasoning with additional salt and pepper if needed, then serve.