Place lentils in a large saucepan; add enough water to cover by 1 inch. Bring water to a boil and cook until tender, about 10 minutes; drain.
Heat olive oil in a saucepan over medium heat. Add garlic, onion, and carrot; cook and stir until the onion has softened and turned translucent, about 5 minutes. Pour in lentils, 1 quart water, oregano, rosemary, and bay leaves. Bring to a boil. Reduce heat to medium-low, cover, and simmer for 10 minutes.
Stir in tomato paste and season with salt and pepper. Cover and simmer until the lentils have softened, 30 to 40 minutes, stirring occasionally. Add additional water if the soup becomes too thick. Drizzle with 1 teaspoon olive oil and red wine vinegar to taste.
