Make the avocado crema by adding avocado, cilantro, scallions, lime juice, salt and pepper to a food processor. Pulse a few times. Drizzle in 1/4 cup olive oil. Pulse again until smooth. Season with more salt, if needed.
Make the blackening seasoning by combining onion powder, paprika, garlic powder, thyme, oregano, salt and pepper together in a small bowl. Mix well.
Using a paper towel or kitchen towel, pat the cod dry; you want to remove as much of the moisture as you can. You do this so the fish develops a beautiful blackened crust.
Sprinkle the blackening seasoning over the cod loins on all sides and press the blackened seasoning into the flesh.
Place a large cast-iron skillet over medium heat. Add butter and oil to the skillet. Because blackening can create a lot of smoke, turn on your exhaust fan and open windows in the kitchen (if possible).
Add the cod to the pan once the pan is hot. Cook for 4-5 minutes (don’t touch the fish during this time), you want a nice blackened crust to develop. Flip fish and cook another 3-4 minutes, or until it flakes easily with a fork and is opaque throughout. This will vary depending on the thickness of your cod loins. Cod is cooked through when the internal temperature reaches just about 140 degrees F in the center of the thickest part of the fillet, as measured with a meat thermometer; the fish will continue to rise in temperature to a safe temp of 145 degrees F. The flesh will turn from translucent to opaque and pearly white and will flake easily with a fork when inserted in the thickest part of the flesh. Remove the cod from heat.
Place lettuce, optional pea shoots, avocado slices and queso fresco on a large platter. Drizzle with avocado crema and sprinkle with cilantro leaves, reserved scallions. Place cod on the platter next to the salad. Serve with lime wedges.