Heat olive oil and 1 tablespoon butter in a 10- to 12-inch cast-iron skillet over medium-high heat.
Combine cumin, paprika, Italian seasoning, salt, and pepper in a small bowl.
Season the salmon, place it skin-side down in the skillet, and cook 4 to 5 minutes until about three-quarters cooked.
Flip the salmon, add the remaining butter, and once melted add the minced garlic.
Whisk honey, soy sauce, and lime juice. Pour over the salmon and cook 2 minutes, spooning sauce over the fillets until cooked through and slightly thickened.
Remove from heat, garnish with green onions, and serve with lime wedges.