In a medium saucepan set over medium heat, add the carrots, olive oil, garlic and onions. Sweat until cooked through, 10 to 15 minutes. Add the oregano, tomatoes, basil and bay leaf. Simmer until the acidity diminishes, 1 hour.
Puree the sauce or leave it chunky (if the vegetables are finely chopped and uniform in size). Season with salt and pepper, and use immediately or cool and reserve for a later use.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.