Heat the olive oil in a medium pot over medium heat.
Add the chopped onion and grated carrot and cook, stirring occasionally, until softened, about 5–7 minutes.
Stir in the minced garlic and crushed red pepper flakes and cook until fragrant, about 1 minute.
Add the crushed tomatoes, tomato paste, kosher salt, black pepper, dried oregano, and granulated sugar; stir until combined.
Bring the sauce to a gentle simmer, then reduce heat to maintain a low simmer and cook, uncovered or partially covered, for 20–30 minutes, stirring occasionally; add a splash of water if it becomes too thick.
Taste and adjust seasoning as needed, then stir in the torn fresh basil just before serving.