Savory Dutch Baby

1 pound cremini mushrooms
4 to 6 cloves garlic
2 tablespoons fresh thyme leaves, divided
2 tablespoons chopped fresh chives, divided
2/3 cup all-purpose flour
2/3 cup whole milk
3 large eggs
1 1/4 teaspoons kosher salt, divided

Freshly ground black pepper
4 tablespoons unsalted butter, divided
1/2 cup grated Parmesan cheese, plus more for serving
2 tablespoons olive oil
1/4 cup low-sodium vegetable broth or white wine
A few handfuls baby arugula

Arrange a rack in the middle of the oven. Place a 10-inch cast-iron skillet on the rack, and heat the oven to 425°F.

Quarter 1 pound cremini mushrooms (slice each quarter in half again for particularly large mushrooms) and transfer to a bowl. Mince garlic, set aside. De-stem thyme leaves until you have 2 tablespoons leaves. Chop chives until you have 2 tablespoons.

Whisk together 2/3 cup all-purpose flour and 2/3 cup whole milk, then add the 3 large eggs, 1/4 teaspoon of the kosher salt, and several grinds black pepper in a medium bowl, mix until no lumps remain. Whisk in 1 tablespoon of the thyme leaves and 1 tablespoon of the chopped chives.

Carefully remove the hot skillet from the oven and immediately add 2 tablespoons of the unsalted butter. Swirl to melt, making sure it coats the bottom and up the sides of the pan. Immediately pour the batter into the hot skillet. Sprinkle with 1/2 cup grated Parmesan cheese.

Bake until golden and puffed and crispy on the edges, 18 to 20 minutes. Meanwhile, heat 2 tablespoons olive oil and 1 tablespoon of the unsalted butter in a large skillet over medium-high heat. Add the quartered mushrooms, toss to coat in the fat, and arrange in a single layer. Sear undisturbed until the bottoms are well-browned, about 3 minutes. Season with the remaining 1 teaspoon kosher salt and several grinds black pepper and sauté until browned and tender, about 5 minutes.

Reduce the heat to medium. Add the minced garlic, remaining 1 tablespoon unsalted butter, and remaining 1 tablespoon thyme leaves. Sauté for 2 minutes more. Add 1/4 cup white wine or broth and cook until mostly evaporated, 2 minutes more. Remove from the heat and stir in a few handfuls of baby arugula, stirring to wilt slightly.

At this point, your Dutch baby should be just about ready. When it’s done, pull it out of the oven and immediately top it with the mushroom mixture. Sprinkle with the remaining 1 tablespoon chives and more Parmesan cheese.  Serve immediately.