In a medium bowl, whisk together the vinegar, garlic, shallot, and mustard. Slowly whisk in the oils until emulsified. Add the herbs, season with salt and pepper, and mix well. Set aside.
Make the salad:
Put the mesclun in a large mixing bowl; set aside. In a large sauté pan, heat 2 Tbs. of the olive oil over high until very hot. Add the chicken and sear well, about 2 to 3 minutes per side. Reduce the heat to medium low and continue cooking until the chicken is done, 5 to 8 minutes, depending on thickness. Transfer the chicken to a cutting board, let rest 5 minutes, and slice thinly on the bias. Add the remaining 1 Tbs. oil to the sauté pan, turn the heat to medium high, and add the mushrooms and red onion. Sauté until tender, about 4 min. Reduce the heat to low, pour in the dressing, and just heat through. Pour the mushroom and onion mixture and about threequarters of the liquid from the pan onto the greens and toss well to gently wilt them. Distribute the salad among four serving plates. Top with the sliced chicken, cheese, and hazelnuts. Drizzle the remainder of the dressing over the chicken and serve immediately.
