Preheat broiler. Toss cubed carrot with 1 teaspoon oil. Sprinkle with salt and pepper.
Spread carrots out on a sheet pan and roast at 400 F until crisp-tender and golden brown in spots, turning frequently. Remove from pan to cool more rapidly.
Whisk ½ cup oil, vinegar, basil, diced tomatoes, garlic and rosemary in small bowl until well blended. Season to taste with salt and pepper.
Add arugula, quartered tomatoes, carrots and pecans to a large salad bowl. Season with salt and pepper.
Toss salad with enough dressing to coat evenly.