Put a baking sheet on the bottom oven rack and preheat to 450 degrees F. Bring a large pot of salted water to a boil. Add the green beans and cook until crisp-tender, about 4 minutes. Drain and rinse under cold water. Pat dry and transfer to a large bowl.
Meanwhile, toss the cauliflower with 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Transfer to the hot baking sheet and roast, tossing once, until tender and golden brown in spots, about 20 minutes.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the bacon and cook until crisp, about 3 minutes. Remove with a slotted spoon to a paper towel?lined plate to drain. Increase the heat to medium high and add the oyster and shiitake mushrooms and the shallots to the skillet; season with 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until tender and golden, 5 to 6 minutes. Stir in the vinegar, parsley and tarragon.
Transfer the mushroom mixture to the bowl with the green beans. Add the cauliflower and bacon; drizzle with the remaining 3 tablespoons olive oil, season with salt and pepper and toss. Serve warm or at room temperature.