Heat 1 tablespoon of olive oil in a skillet over medium heat. Add mushrooms, and cook stirring until soft. Continue cooking until the juices from the mushrooms have reduced to about 2 tablespoons. Stir in the remaining olive oil, balsamic vinegar, salt and pepper until evenly blended. Turn off heat, and let the mushrooms sit in the pan until they are just warm, but no longer hot - otherwise the greens will wilt too much.
Put the baby greens into a serving bowl, and pour the warm mushroom mixture over them. Toss to blend, and serve immediately.