Preheat oven to 425°F. Toss together mushrooms and 1 tablespoon oil on a large rimmed baking sheet. Season with salt and pepper. Bake for 10 minutes. Push mushrooms to one side and add broccoli to pan. Toss with 1 tablespoon oil. Season with salt and pepper. Roast until vegetables are golden brown and tender, 12 to 15 minutes. Meanwhile, heat remaining tablespoon oil in a large skillet over medium heat. Season pork with salt and pepper. Cook until internal temperature on an instant-read thermometer reads 140°F, 4 to 5 minutes per side. Transfer to a platter and tent with foil; reserve skillet. Add shallots to skillet and cook, stirring occasionally, until tender, 3 to 4 minutes. Add flour and cook, stirring, 1 minute. Add wine and simmer until thickened, 2 to 4 minutes. Add stock and simmer until thickened and reduced to about 1/2 cup, 2 to 4 minutes. Remove from heat and stir in crème fraîche, Dijon, and thyme. Season with salt and pepper. Serve pork topped with pan sauce and roasted vegetables alongside.