Working in small batches, place brussels sprouts in feed tube of processor fitted with thin slicing disk; slice.
Melt butter with olive oil in large pot over medium heat. Add shallots; sauté until translucent, about 5 minutes. Add garlic; stir 1 minute. Add brussels sprouts; increase heat to medium-high and sauté until tender, about 8 minutes. Stir in half of pine nuts and lemon juice. Season with salt and pepper. Transfer to bowl. Sprinkle with remaining pine nuts and serve.
Adapted from Bon Appétit, October 2007, Jill Silverman Hough