A modern take on a classic holiday side dish that will make anyone a fan of Brussels sprouts.
Put the butter in a light-bottomed saucepan over medium-low heat (light-bottom is key so that you can see the butter turn brown). Let it melt completely and begin to crackle and foam. Once the foam becomes abundant, start to stir the butter until the foam subsides and you see the butter separate (i.e. particles of milk fat fall to the bottom of the pan). Continue stirring with brief periods of rest until the milk fats turn from white to light brown (this entire process should take about 10-12 minutes). Once the bits of milk fat turn light brown, immediately pull the pan from the heat.
Bring a large, rimmed baking sheet up to temp in a 425° oven. Put 2 tablespoons of the brown butter in a large bowl (reserve remaining) and whisk in 1 tablespoon olive oil. Add the halved Brussels sprouts to the bowl and toss with your hand to coat. Sprinkle 3/4 teaspoon kosher salt over top (reserve remaining salt) and toss again. When ready to roast, pull the hot baking sheet from the oven and pour the Brussels sprouts and brown butter-olive oil coating onto the pan. Quickly distribute the Brussels sprouts across the baking sheet with the halved (flat)-side down. Return the baking sheet to the bottom rack of the 425° oven and let the sprouts roast for 20-25 minutes or until lightly charred on top and bottom.
Meanwhile, transfer the remaining 2 tablespoons brown butter (including any darkened milk fat bits) to a medium sauté pan over medium heat. Add the sliced leek and cook down for 2-3 minutes. Then add the pine nuts, bread crumbs, currants, black pepper, and remaining 1/4 teaspoon salt. Cook (stirring frequently) until the bread crumbs and pine nuts appear lightly toasted (approximately 5-6 minutes). Then turn off the heat and stir in the chopped fresh mint.
Transfer the roasted Brussels sprouts to a large serving platter or bowl and top with the warm pine nut crumble. Add the crumbled feta over top and serve.