Preheat the oven to 450F. Place the oysters on a cookie sheet, ideally on a bed of salt to help keep them level. Bake in the oven for 10 minutes.
Allow to cool slightly before handling. Holding each oyster in a towel and keeping it level (you don't want to spill the brine inside), remove the top shell by sliding a knife around the inside of the slightly open shell, separating the oyster flesh from it. Pop the shell off, inserting the knife (or screwdriver) into the hinge of the shell, if necessary.
In a small saute pan, melt the butter over medium heat. Add the garlic and cook until it is fragrant and starting to turn golden brown, 1-2 minutes. Add the lime zest and the juice from half the zested lime. Set aside.
In a small bowl, toss together the panko and the cheese. Divide the mixture among the shelled oysters. Top with the garlic lime butter, again evenly distributing it.
Turn the oven's broiler to HIGH. Broil for 1-2 minutes, until the cheese has melted and the tops are a golden brown. Serve.