Heat the oil and butter. Heat olive oil and 1 tablespoon butter in a large (10 to 12 inches) cast iron skillet over medium-high heat.
Make the seasoning. In a small bowl combine cumin, paprika, Italian Seasoning, salt, and pepper; mix until incorporated.
Prep and cook the salmon. Season the salmon fillets with the seasoning and transfer them to the skillet, skin side down. (Please see my notes.) Cook the fillets for 4 to 5 minutes, or until they are three-quarters of the way cooked.
Continue to cook. Flip the fish over and add 1 tablespoon of butter to the skillet. (If working in batches, at this point you want to place all your fillets back in the skillet.) Wait until the butter melts, then add the minced garlic to the fish.
Make the honey garlic sauce. In the meantime, whisk the honey, soy sauce, and lime juice together in a bowl until well combined. Pour the prepared honey soy sauce over the fish and continue cooking for 2 more minutes, or until the fish is cooked through and the sauce has slightly thickened. Spoon the sauce over the fillets as they cook.
Finish and serve. Remove from heat. Garnish the salmon fillets with sliced green onions and serve with lime wedges.
Notes
Cook in batches. For the best and easiest results, cook 2 salmon fillets at a time. It’s much easier to flip them over when the pan isn’t crowded. When it’s time to add the sauce, just return all the salmon fillets to the pan and continue with the recipe.
Storage. Keep cooked salmon refrigerated in airtight containers for 2-3 days.