Preheat grill to medium-high heat. Season the beef generously with salt and pepper on both sides.
Grill the meat for 4 to 5 minutes per side for medium-rare, or until it reaches your desired doneness. Remove from grill and let rest for 10 minutes.
While the meat rests, whisk together olive oil, balsamic vinegar, Dijon mustard, salt, and pepper in a small bowl to make the dressing.
In a large serving bowl, combine arugula, halved cherry tomatoes, sliced avocado, blue cheese crumbles, and pickled red onions.
Slice the rested meat thinly against the grain. Arrange the slices over the greens.
Drizzle the vinaigrette over the top and garnish with chopped fresh chives before serving.