Stem the mushrooms and remove the black gills by scraping with a teaspoon. In a small bowl, whisk together the vinegar, roasted garlic, rosemary, sage, and olive oil. Season to taste with salt and pepper. Using a pastry brush, “paint” the mushroom caps liberally with the mixture. Set aside, lightly covered.

Toss the greens with some of the Mustard Seed Vinaigrette and arrange attractively on plates. Drizzle a bit more of the vinaigrette around. Grill the mushrooms quickly over hot coals or in a stove-top grill pan over medium-high heat. Slice the mushrooms thickly on the bias and arrange on top of the greens. Top with Parmesan Chips and serve immediately.

For the Vinaigrette:

In a small bowl, whisk together the mustard, mustard seeds, vinegar, orange juice, dill, and olive oil until just combined. Season to taste with salt and pepper. Prepare at least 30 minutes before serving to allow the flavors to marry.

For the Chips:

To prepare one chip on the stovetop: In a small bowl, combine the cheese and cumin. Heat a large nonstick skillet over medium heat. Sprinkle 2 tablespoons cheese in a lacy round over the bottom of the pan. The cheese will begin to melt and then bubble and lightly brown. Using a fork or spatula, lift by the edges to loosen the chip from the pan. Remove and cool on paper towels for a flat chip. Repeat for the remaining chips.

To prepare multiple chips in the oven: In a small bowl, combine the cheese and cumin. Put the cheese in rounds on parchment or a silicone baking mat on a baking sheet. Bake in a 375°F oven for 6 to 8 minutes or until the chips begin to color. Use a fork to lift the edges and loosen the chips from the pan. Remove and cool on paper towels.

The size of the chip will depend on the amount of cheese you use. Three tablespoons will yield a chip about 4 inches in diameter. Make sure to sprinkle the cheese with a light hand and make them as lacey as possible so that they don’t end up too dense and heavy. You can form the chips by draping over a rolling pin or small overturned bowl.