Rigatoni: Tuscan Chicken Pasta

CHICKEN:
2 boneless skinless chicken breasts, approximately 1 pound
3 tablespoons olive oil, divided
1 teaspoon paprika
1 teaspoon garlic powder
1 teaspoon kosher salt
½ teaspoon black pepper
PASTA:
8 ounces rigatoni pasta noodles, cooked al dente according to package instructions
4 tablespoons (½ stick, 57 g) unsalted butter
¼ cup (40 g) shallot, finely diced
¼ cup (27.5 g) sun-dried tomatoes, softened in hot water and chopped
1 teaspoon garlic minced
2 tablespoons tomato paste
1 teaspoon oregano
1 teaspoon paprika
½ teaspoon garlic powder
½ teaspoon kosher salt
¼ teaspoon black pepper
1 ½ cups (357 g) heavy cream
1 ½ cups (245 g) milk
1 cup (30 g) fresh spinach
1 cup (100 g) parmesan cheese, grated (plus more for garnish)
1 cup (149 g) cherry tomatoes, halved
fresh parsley, for garnish
salt and pepper, to taste