To prepare vinaigrette, in a screw-top jar, combine oil, lemon juice, basil, mustard, garlic, salt, and black pepper. Cover and shake well. Set aside.
In a covered large saucepan cook green beans in a small amount of boiling water for 2 minutes. Add carrots, cook covered, for 8 minutes more or until vegetables are crisp-tender. Drain. Rinse with cold water, drain again.
Place beans, carrots, mushrooms, sweet peppers, and cherry tomatoes in a resealable plastic bag set in a large bowl. Pour vinaigrette over vegetables. Seal bag; turn to coat vegetables. Marinate in the refrigerator for 4 to 24 hours, turning bag occasionally.
To serve, bring vegetables to room temperature. Drain vegetables; arrange on a serving platter. Enjoy!