For the steak, in a gallon-size zipper plastic bag, combine the olive oil, soy sauce, Worcestershire sauce, vinegar, parsley, dry mustard, garlic cloves, and lemon juice.
Add the flank steak, pressing the marinade around to ensure it has moistened all sides of the steak.
Press out excess air and zip the bag shut. Set on a plate and place in the refrigerator to marinate for 1-2 hours.
While marinating, prepare the beets.
Trim the root and leaf from each beet and slice into thin wedges, no more than ½ inch thick. To prevent staining from the beets, wear gloves to protect hands.
Place beets in a large bowl and drizzle with olive oil, salt, and pepper.
Stir to evenly coat and set aside until ready to grill.
Make sure the grill has preheated on high heat. Clean the grates to ensure any charred bits are removed. Remove the marinated steak from the refrigerator 30 minutes before grilling to allow the meat to come to room temperature. At this point, season both sides of the steak with salt and pepper.
Place a grill basket on the grill and start with the beets. Pour the prepared beets in a grill basket, spreading to an even layer. If the basket prevents an even layer, stir and turn the beets every 15 minutes. Allow the beets to grill, stirring once until they begin to become tender, 30-45 minutes.
Grill the steak over high heat until charred, about 6-8 minutes per side for medium-rare (130-135°F) or 8-10 minutes per side for medium (135-140°F).
When done, remove steaks from the grill onto a clean tray. Allow steak to rest 15 minutes before slicing.
Check beets with a knife to ensure they are tender. If a knife inserted into the beet meets no resistance, they are done. Remove beets to a bowl.
While the steak is resting, prepare the dressing for the beets. Add the apple cider vinegar, honey, Dijon mustard, and thyme to the beets, creating a dressing. Stir to combine.
To serve, add a mixture of greens to a large platter or individual plates. Thinly slice the steak, cutting horizontally to the graining, and add to the greens. Top with dressed beets and finish with crumbled blue cheese.