Preheat the oven to 425 degrees F. Toss the mushrooms with 2 tablespoons olive oil, a pinch of salt and a few grinds of pepper on a baking sheet.
Spread out in a single layer. Roast, stirring halfway through, until well browned and crisp around the edges, about 25 minutes. Let cool for a few minutes, then scrape up with a spatula and transfer to a bowl.
Meanwhile, heat the remaining 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat. Add the leek and garlic, season with salt and pepper and cook until the leek softens, about 2 minutes. Add the orzo, 2 cups water, the milk, 1 teaspoon salt and a few grinds of pepper. Bring to a boil, stirring constantly. Reduce the heat to a simmer and cook, stirring occasionally, until the orzo is al dente, 5 to 7 minutes.
Remove from the heat and add the cheese, spinach, lemon juice and 1 tablespoon parsley. Stir until the cheese melts and the spinach wilts; add a splash of water if the mixture is too thick. Season with salt and pepper.
Toss the mushrooms with the lemon zest and remaining 1 tablespoon parsley. Divide the orzo among bowls and top with the mushroom mixture.