Chop the garlic, sprinkle it with a pinch of salt, and mash it into a paste with the side of a chef's knife. Finely grate the zest from half of the lime and then juice the whole lime. In a medium bowl, whisk the garlic, lime zest, 1 tablespoon of the juice, and the mayonnaise. Toss in the cabbage, scallions, and cilantro. Season with 1/4 teaspoon salt and several grinds of pepper.

In a small bowl, mix the chili powder, cumin, 1/4 teaspoon salt, and several grinds of pepper. Sprinkle the spice rub all over the tilapia.

Melt the butter in a 10-inch cast-iron or nonstick skillet over medium-high heat. Cook the tilapia on both sides until browned and cooked through, about 3 minutes total for the small pieces and 5 minutes total for the large pieces. Transfer to a plate. Toss the slaw and add more lime juice, salt, and pepper to taste. Serve the tilapia with the slaw.