In a medium bowl, whisk together the garlic, tahini, lemon juice, and a generous pinch of salt. Add cold water 2 tablespoons at a time and continue whisking until it forms a smooth, saucy consistency. The mixture will seize up at first; just keep adding water and whisking until it smooths out. Taste for seasoning and adjust as needed. Set aside.

Preheat the oven to 425 degrees F. Toss cauliflower with 2 tablespoons olive oil, salt, and pepper, then spread out evenly onto a baking sheet. Bake until the florets are tender and deeply golden brown, about 20-25 minutes.

Heat remaining 2 tablespoons olive oil in a large skillet (well-seasoned cast iron works best) over medium-high heat. Use paper towels to pat the barramundi fillets very dry, then season well with salt and pepper on both sides. Season the skinless side of each fillet with cumin (or only one side if using skinless fillets).

When the oil is shimmering and almost smoking, gently place two fillets in the pan skin-side-down (or the side without cumin). Use a spatula to gently press down on each fillet for about 15 seconds to prevent curling. Cook until almost completely opaque around the edges, then flip and finish cooking for about one additional minute on the other side. You want the majority of cooking to happen while the fish is skin-side-down in order to achieve the crispiest skin possible. Repeat with remaining fillets.

Divide the tahini sauce between 4 plates, then top with cauliflower. Place the barramundi fillets skin-side-up on top of the cauliflower, sprinkle pomegranate arils and mint around the plates, then serve immediately.