Stir together first 4 ingredients, 1/3 cup vinaigrette, and 1/4 teaspoon pepper in a medium bowl. Cover and chill 30 minutes.
Place flank steak and remaining balsamic vinaigrette in a large zip-top plastic freezer bag; seal and chill 30 minutes, turning steak occasionally.
Remove steak from marinade, discarding marinade. Sprinkle steak evenly with salt and remaining 1/2 teaspoon pepper.
Grill steak, covered with grill lid, over medium-high heat (350° to 400°) 5 to 6 minutes on each side or to desired degree of doneness. Let stand 10 minutes. Cut steak diagonally across the grain into thin strips.
Divide lettuce evenly among 4 bowls. Top each evenly with bean mixture and steak. Sprinkle with cheese.
*Cannellini beans may be substituted.
Marian's tip: For an easy appetizer or a simple sandwich stuffing, finely chop the vegetables in the white bean mixture. Serve alone with toasted pita chips, or stuff inside a pita pocket with flank steak or thinly sliced roast beef.