1. Whisk together first 5 ingredients in a small bowl. Gradually whisk in olive oil; stir in salt and pepper. Pour 1/3 cup marinade into a zip-top plastic storage bag. Add mushrooms and steak, turning to coat; seal and chill 1 1/2 hours. Stir blue cheese into remaining vinaigrette. Cover and chill until ready to serve.
2. Preheat grill to medium-high heat (350° to 400°). Remove mushrooms and steak from marinade, discarding marinade; grill steak 5 to 6 minutes on each side (for medium-rare) or until desired degree of doneness. Let stand 5 minutes. Grill mushrooms 3 to 4 minutes or until tender. Slice steak.
3. Top arugula with mushrooms, steak, tomatoes, and toasted pecans. Drizzle with vinaigrette.