Hi @LAgirl -
How’s it going with your new grill pan? 
I made these and thought you might like to see the results and my thoughts & pics. These are San Lucas Ribeyes from Yummy Market on S.Vicente & Hauser. The thinness make these great for the grill pan and the fatty keeps them from drying out. Note: they don’t do well if previously frozen.
Seasoned w/Salt, Adobo Seasoning, Smoked Paprika.
Pre-heated pan on high 10+ minutes, then oiled pan (not meat), seared steaks for 3 minutes one side & 2 minutes on the flip side. Easy peasy.
I’ve been doing a little experimenting since the discussions on this thread. Thoughts: my pan is finally seasoned enough so no more oiling the meat (pan only) and the dried spices cause good smoking which imparts good flavor. 
I tried cooking steaks on medium, pre-heating pan for 10-15 minutes. The results were mixed. I think it might work better for thicker steak. The thin came out tender & somewhat juicy, but not smokey or crispy, as the fat doesn’t render enough on medium, and the insides cooked thru while trying to render and crisp up the fat (not a problem if you don’t like a little pink). High is working for me. 
Steak Bowl - Rice, Tomato, Grilled Onions, Avocados
With Dressing - Fresh Salsa Verde, Spicy Aguachile Liquid, Lime, Grapeseed Oil, Garlic, Cilantro, Salt
