Let 2 pints gelato sit at room temperature to soften slightly. Meanwhile, split 6 brioche buns and toast them.
Melt 1 tablespoon unsalted butter in a 12-inch heavy-bottomed skillet (preferably cast iron) over medium heat and swirl the pan so the bottom is coated.
Add 2 sets of buns cut-side down and cook until toasted and golden-brown, 2 to 3 minutes. Transfer to a cutting board cut-side up and sprinkle with a pinch of flaky sea salt.
Repeat toasting the remaining buns in two more batches, adding 1 tablespoon unsalted butter to the pan before each batch.
Let all the toasted buns cool for 5 minutes.
Top each bottom half of the brioche buns with 1/3 pint of gelato (about 2 scoops).
Press the top buns gently on top to adhere and serve immediately.