Preheat oven to 450˚F. Line a baking sheet with parchment paper.
For sprouts, slice off the dirty end of the sprouts and then cut in half through the stem. Place on the baking sheet, cut side up. Drizzle sprouts with olive oil and season with salt and pepper. Roast for 20 minutes.
Meanwhile, make brown butter sauce. Add butter to a small saucepan over low heat. Melt butter and continue to heat until butter is foaming. After 5-6 minutes, you'll notice brown bits on the bottom of the pot. Stir occasionally. When butter has browned bits and is nutty fragrant, remove from heat and add lemon juice and dried sage.
After sprouts roast, place them in a bowl and toss with about 2/3s of the brown butter sauce. Toss well to combine and return to baking sheet cut side up. Roast for another 10-15 minutes until deeply roasted.
For serving, drizzle sprouts with extra butter sauce if they seem dry (optional) and garnish with flakey salt and lemon zest.