Preheat oven to 400ºF. Rub chicken with oil and salt and pepper to taste. Place on baking sheet and bake for 12-16 minutes, depending on size and thickness of chicken, until meat is just cooked through. Set aside to cool.
Meanwhile, cook pasta in large stockpot according to package directions. Salt the water with 1 tablespoon salt and cook to al dente, or slightly chewy. When draining pasta, place colander over large bowl to reserve pasta water.
In stockpot, melt butter over medium-low. Add garlic and cook until fragrant, about 2 minutes. Add tomatoes, artichoke hearts and red pepper flakes. Stir to combine.
Chop chicken into bite-sized pieces and add to stockpot.
Pour pasta into pot and give it a good stir to mix up the ingredients. Turn heat up to medium and add pasta water, cream and cheese. Add the liquids and the cheese half a cup at a time, stirring briefly before adding the next batch.
Add spinach and stir, cooking until spinach wilts. Lightly squeeze half a lemon over the pot, stir and taste, adding more salt or pepper if necessary.
Serve and garnish with parsley, a lemon slice or more cheese.