Bring a pot of salted water to a boil. Cook the green beans until tender, about 6 minutes. Drain and plunge into a bowl of ice water to cool. Drain again.
In a large skillet, melt the butter with the oil over medium-high heat. Add the shallots and sauté for 1 minute. Reduce the heat to medium-low; sauté until the shallots are browned and tender, about 20 minutes. Sprinkle with thyme, salt and pepper.
Add the cooked green beans to the shallots and stir over medium-high heat until heated through. Season to taste with additional salt and pepper. Serve warm.
Notes
Time saver: Prepare the green beans ahead of time in step 1. Wrap in paper towels and seal in a large zip bag. Keep in the refrigerator for up to 1 day.