Don't cook the onions too fast. You want them caramelized, not heavily browned.
Brush steaks with olive oil, sprinkle with salt and pepper and set aside one hour before grilling. Allow 30+ minutes to caramelize onions. In a saute pan over low to medium 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.