Mince garlic and mash to a paste with salt. In a bowl whisk together garlic paste, shallot, and vinegar and add oil in a stream, whisking until emulsified. Vinaigrette may be made 2 days ahead and chilled, covered. Bring vinaigrette to room temperature and whisk well before using.
Trim arugula and tear leaves in half. In a bowl toss together arugula, tomatoes, and carrot.
Just before serving, drizzle vinaigrette over salad and toss with salt and pepper to taste.
