Combine all marinade ingredients in a ziplock bag with the mushrooms and gently swish the marinade around the mushrooms. Marinate in the bag for at least 20 minutes, and up to 4 hours.
Preheat the oven to 400 °F, or heat up the grill.
Grill the mushroom over direct heat on a grill, or bake on parchment paper for 20-25 minutes, flipping partway through.
Combine the dressing ingredients in a small bowl with a fork. I like to mix dressing in a small jar with a lid so it can be shaken and emulsified. Toss the salad with the veggies.
When the mushrooms are done, let cool for a few minutes and slice into thick meaty slices. Lay them on top of the salad.