Sauteed Black and Green Olives: Olive Neri e Verdi

Name: Sauteed Black and Green Olives: Olive Neri e Verdi
Ingredients: 1/4 cup extra-virgin olive oil; 2 cloves garlic, chopped; 1/2 pound small green brine-cured olives, like arbequina, drained and rinsed; 1 cup Basic Tomato Sauce, recipe follows; 1 Spanish onion, chopped in 1/4-inch dice; 4 garlic cloves, peeled and thinly sliced; 3 tablespoons chopped fresh thyme leaves, or 1 tablespoon dried; 1/2 medium carrot, finely shredded; 2 (28-ounce) cans peeled whole tomatoes, crushed by hand and juices reserved; Salt