Begin with the onions because they will take about 45-50 minutes to cook. They are well worth the time!
Heat a medium frying pan with olive oil and cook the onions on a medium high heat until they begin to soften (about 5-10 minutes). Sprinkle with salt and pepper to taste and turn the heat down to medium (do this sooner if the onions are browning). If the pan is looking dry or the onions are sticking, add a splash of chicken or vegetable broth.
After 30 to 35 minutes, add in the wine, lemon juice and garlic when the onions are lightly browned and translucent. Turn the heat down even more if the onions are sticking or frying instead of caramelizing. Add more broth if they need to cook more and the pan becomes dry.
After about 45 minutes of cooking, add in the creme fraiche and dijon mustard. Let it heat through and stir in the tarragon when you are ready to serve.
Heat a large stock pot with water and salt to a boil. Add the green beans and allow them to cook for 2-3 minutes. Drain the water and place the beans in a serving dish. Pour the caramelized onion mixture on top of the green beans, garnish with toast fresh breadcrumbs, parmesan cheese or crispy mushrooms.