Use a food processor fitted with a slicing disk to thinly slice the Brussels sprouts. (Alternatively, slice thinly by hand or with a mandoline.) Set aside.
In a large skillet over medium heat, heat the oil. Add the shallots and cook, stirring occasionally, until almost translucent, about 3 minutes.
Add the garlic and cook, stirring occasionally, for 1 minute.
Add the Brussels sprouts and cook, stirring occasionally, until tender, about 8 minutes.
Remove from heat and add the lemon juice, dill, and 3 tablespoons of the almonds, scraping up any browned bits in the skillet.
Add salt and pepper to taste.
Transfer to a serving bowl or plates, sprinkle with the remaining 1 tablespoon of almonds, and serve.
