Heat oil in Dutch oven on medium-high. Add carrots, and season with salt, if desired. Cook 5 minutes, stirring once or twice, or until carrots are crisp-tender and lightly browned.Stir in ginger, then tomatoes and 3 large basil leaves. Bring to a simmer, reduce heat to medium-low, and cook 10 to 12 minutes, or until carrots are fork-tender. Stir in remaining basil leaves.