Cut off and discard ends from shallots. Cut shallots lengthwise in half, then remove peel with paring knife. Melt butter with oil in heavy large skillet over medium-high heat. Add shallots and sauté 1 minute. Reduce heat to medium-low; sauté until shallots are browned and tender, about 20 minutes. Sprinkle with thyme. Season to taste with salt and pepper. DO AHEAD Can be made 2 hours ahead. Cover loosely with foil and let stand at room temperature.