Heat a large sauté pan over medium-high heat. Add 1 tablespoon butter and the olive oil. When the butter is foaming, add the sliced mushrooms in a single layer (work in two batches if necessary). Let them cook undisturbed 2–3 minutes to develop browning, then stir. Add the remaining 1 tablespoon butter, minced garlic, thyme, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Cook another 2–3 minutes until mushrooms are golden and any released liquid has mostly evaporated. Remove mushrooms to a bowl and keep warm.

Wilt arugula

If serving hot, wipe the pan and return to medium heat. Add the arugula and a pinch of salt, tossing 30–45 seconds just to wilt slightly but remain bright green. Remove and reserve with mushrooms.

Parmesan Cream Sauce

Make roux

In a medium saucepan over medium heat, melt 2 tablespoons butter. Sprinkle in 2 tablespoons flour and whisk constantly for 1–2 minutes to cook the raw flour taste without browning (you want a blond roux).

Add liquids

Slowly whisk in 1 cup whole milk until smooth, then add 1/2 cup heavy cream. Continue to whisk and bring the mixture to a gentle simmer. Cook 3–4 minutes until the sauce begins to thicken and coats the back of a spoon.

Finish sauce

Lower heat to low. Whisk in 3 ounces grated Parmesan until melted and fully incorporated. Season with 3/4 teaspoon kosher salt, 1/4 teaspoon black pepper, and 1/8 teaspoon freshly grated nutmeg. Taste and adjust seasoning. If sauce is too thick, whisk in up to 2 tablespoons more milk to reach desired consistency. Keep warm over the lowest heat, stirring occasionally to prevent skin formation.

Assembly & Finish

Combine mushrooms and sauce: Add the sautéed mushrooms (and any accumulated juices) to the warm Parmesan cream sauce and stir to combine. Simmer together 1–2 minutes so flavors meld.

Incorporate fontina: Stir in the shredded fontina in small handfuls, allowing each addition to melt fully into the sauce for a smooth, nutty melt. If the sauce tightens up, add 1–2 tablespoons warm milk to loosen.

Add arugula and finish: Fold in the wilted arugula just to combine (if you prefer it crisper, add raw arugula just before serving). Taste and add up to 1/2 teaspoon lemon juice to brighten, if using. Adjust salt and pepper to taste.

Serve: Spoon the Montana Mushroom mixture over pasta, polenta, toasted bread, or as a topping for grilled chicken. Sprinkle with additional grated Parmesan and a crack of black pepper. Serve immediately.