Preheat grill to high (450°F to 500°F). Sprinkle flank steak with 1 teaspoon each of the salt and pepper. Let stand at room temperature 30 minutes.

Meanwhile, spread 1 tablespoon of the oil over cut sides of green tomato halves, and sprinkle with remaining 1⁄2 teaspoon each of salt and pepper. Grill tomato halves, covered and turning halfway through, until charred on both sides and slightly tender, 12 to 14 minutes. Remove from grill; place in a large bowl. Cover with plastic wrap, and let stand until cool enough to handle, about 5 minutes.

Peel and discard skin from charred tomato halves; place tomato halves, vinegar, and honey in a blender or food processor. Process until tomato is finely chopped but not smooth. Pour into a medium bowl, and whisk in mustard. Add remaining 4 tablespoons oil in a slow, steady stream, whisking constantly until smooth. Set vinaigrette aside.

Grill steak, covered and turning once, until charred on both sides and a meat thermometer inserted into thickest portion of steak registers 120°F or to desired degree of doneness, about 4 minutes per side. Let steak rest 10 minutes. Cut diagonally across the grain into thin strips.

Arrange mixed greens, arugula, heirloom tomato wedges, cherry tomato slices, and red onion on a large serving platter. Top with sliced steak, and drizzle with desired amount of vinaigrette.