Heat the olive oil in a large skillet or saucepan over medium heat.

Add the diced carrots and cook, stirring, until tender, about 5-8 minutes.

Add the minced garlic and cook, stirring, until fragrant, about 30 seconds to 1 minute.

Add the tomatoes (freshly grated or canned), sugar, basil sprig, salt, tomato paste, and oregano (if using).

Stir to combine and increase the heat until the sauce begins to bubble.

Reduce the heat to medium and cook, stirring often, until the sauce has thickened and become fragrant, about 20-25 minutes.

Remove the basil sprig.

Taste and adjust seasonings as needed.