Heat a small saucepan over medium heat. Add 1 tablespoon of the oil and heat another 30 seconds. Add the shallot and cook, stirring often, until soft and fragrant, about 2 minutes. Add the maple syrup and the vinegar and bring to a simmer. Simmer for 15 minutes to reduce slightly. Remove from the heat and stir in the cranberries.
Meanwhile, heat a large skillet over medium-high heat. Add the remaining 3 tablespoons olive oil and warm another minute. Add the Brussels sprouts to the skillet and cook, undisturbed, until browned and beginning to soften, about 3 minutes. Season with the salt. Stir the sprouts and cook another 3 minutes to continue to brown. Stir again and cook another 3 minutes to brown evenly. Add the maple mixture to the skillet and toss well to coat. Bring to a simmer and simmer to reduce the glaze slightly, another 2 minutes. Serve warm.