AT HOME (MAKE SAME DAY)
Heat 2 tbsp. oil in a large frying pan over medium heat. Add onions and cook, without moving, until golden brown (reduce heat if they get too dark too fast). Carefully turn onions over and let cook until dark golden on both sides and softened inside, about 30 minutes total. Let onions cool, then transfer to a container.
Meanwhile, bring a pot of generously salted water to a boil. Cook beans until bright green and tender, 6 to 10 minutes. Drain and return to pot. Add 2 tbsp. butter, stirring just until melted. Put in a container for transport.
AT THE PARTY
Heat remaining 2 tbsp. oil in a medium frying pan over high heat. Add mushrooms; reduce heat to medium and cook, stirring occasionally, until mushrooms release all their liquid and start to brown and crisp, about 10 minutes. Add remaining 4 tbsp. butter to pan. When butter has melted and begins to sizzle, add shallots, thyme, salt, pepper, and reserved caramelized onions. Cook, stirring gently, until shallots have softened. Add broth and bring to a simmer.
Meanwhile, rewarm beans and transfer to a large platter. Pour mushroom mixture over center of beans.
*For tips on cleaning mushrooms, watch our video at sunset.com/cleanmushrooms.