Fill bottom of a medium saucepan with 1-inch of water. Insert vegetable steamer basket into bottom of saucepan, cover with lid and bring water to boil over medium-high heat. When water starts to boil, place green beans in steamer basket; cover with lid. Steam green beans just until fork tender, about 6 to 8 minutes. Pull basket out of saucepan and allow beans to drain; set aside.
While beans are steaming, in a small skillet melt butter over medium heat, swirling skillet often until butter becomes golden brown, about 4 minutes. Watch closely to prevent burning. Hold over low heat to keep warm.
Meanwhile, in a large nonstick skillet, heat olive oil over medium-high heat. Add mushrooms and onion and sauté for 5 minutes. Add garlic and salt and sauté 1 minute more.
To serve, place green beans onto serving plate, drizzle browned butter over beans and spoon mushroom mixture on top. To garnish, sprinkle with blue cheese and toasted pine nuts.
If you prefer to toast the pine nuts yourself, place nuts in a small skillet over medium heat. Shake skillet often until pine nuts are golden all over, about 4 minutes. This can be done ahead of time.