Bring a large pot of salted water to a boil. Add the 12 oz penne pasta and cook according to package instructions until al dente, usually about 9-11 minutes. Drain the pasta and set aside, reserving a cup of pasta water for later.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the diced chicken breast, seasoning with salt and pepper. Cook, stirring occasionally, until the chicken is golden and cooked through, about 6-8 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Then add the halved cherry tomatoes, dried basil, and dried oregano. Cook for 3-4 minutes, allowing the tomatoes to soften and release their juices.
Add the cooked penne pasta and chicken back into the skillet. Toss in the baby spinach and stir everything together. If the mixture seems dry, add a splash of the reserved pasta water to loosen it up and create a light sauce.
Gently fold in the cubed fresh mozzarella cheese. Reduce the heat to low and cover the skillet for 2-3 minutes, allowing the mozzarella to melt into creamy pockets throughout the dish.
Remove the skillet from heat. Finish with a sprinkle of freshly cracked black pepper and garnish with fresh basil leaves. Serve immediately and enjoy the comforting, cheesy goodness!