Brush steaks with olive oil, sprinkle with salt and pepper and set aside 1 hour before grilling. Allow 30+ minutes to caramelize onions. Using a medium high heat, melt butter, 2 T olive oil and sliced onions, thyme, a pinch of salt and stir occasionally. After about 30 minutes, add honey and balsamic vinegar and cook for about 5 more minutes. Spoon onions into a bowl and set aside. Slice blue cheese and set aside.
Heat grill to medium high and brush grates with oil. Grill steaks for 5-10 minutes per side. Internal temperature for medium rare is 125 degrees. Let steaks rest for 5-8 minutes.
Place rib eye steaks on a platter or individual plates, spoon over caramelized onions and top with a slice of blue cheese. Serve immediately. Serves 4.