Bring a large pot of salted water to boil for the pasta. Salt it generously.
Heat olive oil in a large skillet over medium-high heat until shimmering. Add minced garlic and cook for 90 seconds until fragrant and barely golden. Watch carefully to avoid burning.
Add diced tomatoes with their liquid, oregano, basil, salt, black pepper, and red pepper flakes (if using). Stir in chicken broth and tomato paste, making sure the paste dissolves completely.
Bring to a gentle simmer and cook for 5 minutes, allowing flavors to blend and liquid to reduce slightly.
Reduce heat to medium-low. Cut softened cream cheese into small cubes and add to the sauce. Whisk continuously until completely melted and smooth.
Add half of the Parmesan cheese to the sauce, whisking constantly to prevent clumps. Reserve remaining Parmesan for serving.
Cook spaghetti in boiling water according to package directions, minus 1 minute for al dente texture. Don't rinse after draining.
Transfer drained pasta directly to the skillet with sauce. Toss with tongs until every strand is coated in creamy tomato sauce.
Serve immediately in warm bowls, topped with remaining Parmesan cheese.