Heat olive oil in a large deep skillet or pot over medium-high heat.
Add the chicken pieces to the skillet and season with salt, black pepper, and dried Italian seasoning.
Cook the chicken for 5 to 6 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for 1 minute until fragrant, stirring constantly to prevent burning.
Pour in the chicken broth and whole milk, scraping the bottom of the skillet to loosen any browned bits.
Add the uncooked penne pasta to the skillet and stir to combine.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered for 12 to 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 in the grated Parmesan cheese and fresh baby spinach leaves.
Cook for an additional 2 minutes, stirring until the spinach wilts and the cheese melts into a creamy sauce.
Remove from heat and sprinkle chopped fresh parsley over the pasta before serving.