For the beef: Put the beef in a resealable plastic bag. Mix together the olive oil, mustard, garlic and thyme in a small bowl. Pour over the beef, seal the bag and refrigerate for anywhere from 20 minutes to overnight. Take the meat out of the refrigerator about 30 minutes before you are ready to cook.
To cook, heat a grill pan over medium-high heat. Wipe the meat dry and season well with the salt and lemon pepper. Grill the meat for about 4 minutes per side, depending on how you like your beef cooked. Cover and set aside to rest for 15 to 20 minutes before serving.
For the salad: In a jar, shake together the olive oil, mustard, thyme leaves, lemon juice and a pinch each salt and pepper. Add 1 or 2 tablespoons of heavy cream and shake again. Add 2 tablespoons of the blue cheese crumbles and shake once more. Set aside while you assemble the salad and slice the meat.
Put the spinach, romaine and salad greens in a large bowl. Add the tomatoes, scallions, red pepper and red onion. Season lightly with salt and pepper. Toss with a little of the dressing. Add the remaining blue cheese crumbles (about 2/3 cup) and toss again.
To serve: Slice the beef thinly against the grain. Place a pile of the salad on 1 big platter and drape the meat over the salad. Serve extra dressing on the side.