Brussels Sprouts with Lemony Horseradish Sauce

From Keys to the Kitchen by Aida Mollenkamp.
Ingredients:
1 lb. small brussels sprouts, trimmed and halved
1 Tbsp. olive oil
2 shallots, halved lengthwise and thinly sliced crosswise
Kosher salt
3/4 c. low sodium vegetable broth
Zest and juice of 1/2 lemon
1 Tbsp. prepared horseradish
1 Tbsp. unsalted butter

Fill a large bowl halfway with ice water and set aside. Bring a large pot of heavily salted water to a boil over high heat. Add the brussels sprouts and cook until bright green, 2 to 3 minutes. Drain and plunge into ice water until cool. Drain again and dry thoroughly.
Heat the oil in a large frying pan over medium-high heat. When it shimmers, add the shallots, season with salt, and cook until browned, about 5 minutes. Add the brussels sprouts cut-side down and cook, undisturbed, until browned, 4 to 5 minutes.
Add the broth, partially cover, and decrease the heat until the liquid is simmering. Cook until the cores of the brussels sprouts are knife-tender and the broth is slightly reduced, about 3 minutes.
Remove from the heat, add the zest, juice, horseradish, and butter and stir to coat the brussels sprouts. Taste, adjust seasoning as needed, and serve.