In a small bowl, whisk together the avocado oil mayonnaise, lemon juice, and lemon zest to create the aioli, then set aside.
In a shallow dish, combine the smoked paprika, garlic powder, onion powder, cayenne, oregano, thyme, sea salt, and black pepper.
Pat the catfish fillets completely dry with a paper towel and coat both sides generously with the Cajun spice mixture.
Heat the avocado oil in a cast-iron skillet over medium-high heat until it begins to shimmer.
Carefully place the catfish in the skillet and sear for 3 to 4 minutes per side until the crust is dark and the fish flakes easily with a fork.
While the fish cooks, steam the broccoli florets over boiling water for 5 minutes or until tender-crisp.
Serve the blackened catfish immediately, topped with a dollop of lemon aioli and the steamed broccoli on the side.