In a small bowl, whisk the lemon juice, oil, garlic, red pepper flakes, and rosemary. Pour the marinade into a large resealable plastic bag and add the chicken. Press the air from the bag, seal, and turn it a few times to coat the chicken in the marinade. Refrigerate for 30 minutes and up to 8 hours.

In a dutch oven or a wide, deep skillet, heat 1 teaspoon of olive oil over medium-high heat. Remove the chicken breast tenderloins from the bag, discarding the marinade, and add them to the pan. Cook, turning to brown on all sides, until no longer pink and cooked through, about 10 minutes. Transfer the chicken to a plate.

Add 1 ½ cups of the broth to the pan, followed by the penne, vodka sauce, cherry tomatoes, garlic, and shallot. Bring to a boil. Cook, reducing the heat if necessary to keep the pan at a simmer, and stir frequently, taking care to incorporate the sauce that begins to form around the edges of the pan (it will thicken the quickest), until the penne has absorbed most of the liquid and become tender. *If you notice that the pan is becoming dry at any time or that the penne needs more moisture, add more broth ¼ cup at a time, stirring after each addition.

Once the penne is tender and a thick sauce is coating each noodle, turn off the heat, return the chicken to the pan, and gently toss. Stir in the basil. Serve with grated Parmesan cheese.