Adjust rack to top position and preheat oven to 400 degrees. Bring a large pot of salted water to a boil. Wash and dry all produce. Zest and quarter lemon. Cut tomatoes into ½-inch-thick wedges.
Line a baking sheet with foil. Arrange tomato wedges on prepared sheet, skin sides down. Drizzle with olive oil and season with salt, pepper, and 1 tsp Tuscan Heat Spice (save the rest for step 4). Roast on top rack until softened and beginning to release their juices, 20-25 minutes.
Once tomatoes have roasted 10 minutes, add spaghetti to pot of boiling water. Cook until al dente, 9-11 minutes. Reserve ½ cup pasta cooking water (1 cup for 4 servings), then drain. Set spaghetti aside in strainer; keep pot handy for use in step 5.
Pat chicken dry with paper towels; season all over with salt, pepper, and remaining Tuscan Heat Spice. Heat a drizzle of oil in a large pan over mediumhigh heat. Add chicken and cook, stirring occasionally, until browned and cooked through, 4-6 minutes. Turn off heat.
Melt 1 TBSP plain butter (2 TBSP for 4 servings) in pot used for spaghetti over medium-low heat. Add lemon zest, cream cheese, and ⅓ cup reserved pasta cooking water (¾ cup for 4); whisk until smooth. Stir in spaghetti, garlic herb butter, juice from half the lemon (whole lemon for 4), and half the Parmesan. (TIP: If pasta seems dry, add more reserved pasta cooking water a splash at a time until coated in a creamy sauce.) Stir in chicken and season with salt and pepper.
Pick basil leaves from stems; discard stems and roughly chop or tear leaves. Divide spaghetti between bowls and top with tomato wedges. Garnish with basil leaves and remaining Parmesan.