Chef John Fraser of Dovetail Restaurant located in New York City offers the following tips for this recipe. "Make sure the mushrooms are brushed rather than washed. Use a pastry brush or damp towel until they are clean to the eye. Make sure that the oil begins to smoke before adding the maitakes to the pan. This will ensure a crunchy texture." For the squash, he says, "Make sure to cook the squash until the skin is al dente. It will continue to cook as it cools upon taking it out of the oven."
Note: You can make and cook everything earlier in the day. Just make sure not to add dairy or herbs to the barley risotto until you reheat it.
Preheat the oven to 350 degrees.
Clean the mushrooms well using a pastry brush or damp towel. Cut into 4 large pieces. If you can only find small maitakes, leave pieces as large as possible. Set aside.
Slice the delicata squash crosswise into 1-inch-thick rings. Remove the seeds. Toss in a large bowl with honey and olive oil, and season with salt, to taste. Lay flat on a baking sheet and cook for 20 minutes. The squash should be tender, but not mushy. Set aside, but do not remove from the pan.
Cook the barley according to the package directions. Drain and set aside any excess water. Keep the barley warm.
Heat a large ovenproof sauté pan over high heat. Add ¼-inch canola oil. As soon as the oil starts to smoke, carefully place the mushrooms in the pan. Do not move. Reduce the heat to medium-high. Once the mushrooms become brown on one side, drain the oil and flip the mushrooms over. Add the thyme, garlic, and half of the butter to the pan. Put in the oven for 5 minutes. (If your mushrooms are in small pieces, it may take less time.)
Meanwhile, place the pan of squash back in the oven to warm. Reheat the barley with the crème fraîche, remaining butter, and Parmesan. Add the reserved cooking water if the barley is too thick. Add the chopped herbs. Season with salt, to taste.
Remove the mushrooms from the oven and lay on a paper towel. Season with salt, to taste. To assemble, place 2 slices of delicata squash on each plate. Spoon the barley risotto onto the squash rings. Add the mushrooms and additional Parmesan on top.