Cut chicken into bite-sized pieces and place into a mixing bowl.
Add lemon zest, lemon juice, and 2 tbsp. pesto and stir to combine. Allow to sit for 30 minutes and up to 24 hours in the fridge.
On the stove, heat oil in a pan over medium-high heat. Add chicken pieces in a single layer and brown on all sides until cooked through. Once cooked, set chicken on a plate to the side.
While the chicken is marinating, prepare pasta according to the packaging instructions. Before you drain it, be sure to reserve ½ cup of pasta water for use in the sauce later.
To the same pan, reduce heat to medium and add minced garlic and shallot. Cook for one minute until fragrant.
Add cherry tomatoes and cook for 2-3 minutes until they just start to blister. Remove to a plate to the side.
To the same pan, deglaze with reserved pasta water, scraping up any bits of flavor stuck to the bottom on the pan.
Add heavy cream, the remaining pesto and parmesan cheese. Stir to combine and reduce for a minute.
Add in pasta, as well as cooked tomatoes, chicken pieces, mozzarella balls, and chopped basil.
Give everything a final stir before serving.