FOR THE DRESSING: Whisk all ingredients together in small bowl; set aside.
FOR THE BRUSSELS SPROUTS: Fit food processor with slicing disk. Slice brussels sprouts, then transfer to large bowl. Add salt and pepper and toss to combine.
Heat 3 tablespoons oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add half of sprouts in even layer and cook without moving them until sprouts are well browned on bottom and bright green on top, 6 to 8 minutes. Transfer sprouts to serving platter, spread into even layer, and drizzle with half of dressing. Repeat with remaining 3 tablespoons oil and remaining sprouts, layering second batch of cooked sprouts on top of first batch, then drizzle with remaining dressing. Sprinkle with almonds. Serve.
