Preheat the oven to 400˚F. Arrange the pecans in a single layer on a rimmed baking sheet, and toast in the oven until deep brown and fragrant, about 8 minutes. Transfer to a dish to cool.
Bring a medium pot of water to a boil over high heat. Add a couple of generous pinches of salt, then add the Brussels sprouts and cook over high heat until just soft when pierced with the tip of a paring knife, 3-5 minutes. Drain and set aside until cool enough to handle. Slice in half lengthwise, and set aside.
Heat the butter and oil in a large, heavy skillet over medium-high heat. Add the onions and sauté, stirring often, until golden, about 5 minutes. Stir in the garlic and halved Brussels sprouts and sauté, stirring frequently, about 5 minutes, until the Brussels sprouts are golden brown in spots. Fold in the pecans. Season to taste with salt and pepper, and serve.