Bring a large pot of salted water to boil. Cook ditalini according to package instructions until al dente.
Meanwhile, in a large saucepan, heat olive oil over medium heat. Add onion, carrots, and celery. Sauté until softened (5-7 minutes).
Add minced garlic, cook for 1 minute until fragrant.
Pour in crushed tomatoes and broth. Season with salt, pepper, and red pepper flakes if desired.
Simmer sauce for 10-12 minutes until slightly thickened.
Drain pasta, reserving 1 cup of pasta water.
Add pasta to sauce, stir to combine. Add Parmigiano-Reggiano cheese and stir until creamy.
If needed, add reserved pasta water to reach desired consistency.