For vinaigrette, combine oil, lemon juice, basil, garlic, mustard, salt, and pepper in a screw-top jar. Cover and shake well. Set aside.
Cook green beans, covered, in a small amount of boiling water in a large saucepan for 4 minutes. Add carrots and cook, covered, for 8 minutes more or until vegetables are crisp-tender. Drain and rinse with cold water.
Cut shapes out of the sweet peppers, using a star-shape cutter. Place the green beans, carrots, sweet peppers, mushrooms, and tomatoes in a bag set in a large bowl. Pour vinaigrette over vegetables.
Seal bag, and refrigerate for 4 to 24 hours, turning the bag occasionally to distribute vinaigrette.
To serve, bring to room temperature. Drain vegetables; arrange on a platter.