Brussels Sprouts with Brown Butter and Sage

2 pounds fresh Brussels sprouts (40 to 50 sprouts), trimmed and halved
3 tablespoons butter
1/4 cup coarsely chopped sage leaves (6 to 8 leaves)
1 teaspoon kosher salt
1/2 teaspoon freshly ground black pepper

In a large saucepan, add the sprouts to boiling salted water and cook until bright green and just tender, 6 to 8 minutes; drain and set aside.
In a 12-inch skillet, over medium heat, melt the butter and cook until nutty brown in color, being careful not to burn it. Add the sage, stirring until fragrant, about 1 minute. Add the sprouts, salt, and pepper. Toss to coat in the butter and cook until heated through, 5 to 7 minutes.