Bring a large pot of salted water to a boil; cook the penne according to package directions until al dente. Drain in a colander and set the pasta aside.
While the pasta cooks, heat 2 to 3 tablespoons of the olive oil in a very large deep-sided skillet over medium-high heat.
Add the diced Vidalia onion and sauté for about 3 minutes, stirring occasionally, until it begins to soften.
Add the bite-sized chicken pieces, sprinkle with kosher salt and black pepper, and sauté about 5 minutes, stirring and turning occasionally, until the chicken is cooked through.
Add the minced garlic and cook for about 1 minute, stirring nearly continuously, until fragrant.
Pour in the lemon juice and stir to combine.
Turn off the heat and add the drained pasta and baby spinach to the skillet. Toss well to combine, adding the remaining olive oil as needed so the mixture tosses easily and the spinach wilts.
Taste and adjust seasoning with additional salt and pepper if needed (the recipe used about 2 teaspoons salt and 1½ teaspoons pepper total for the full batch).
Sprinkle the shredded Parmesan evenly over the pasta; either leave it on top or stir it in for a cheesier dish, then serve immediately.