Preheat oven to 425°. Line a large rimmed baking sheet with parchment paper.
Place prosciutto slices in a single layer on prepared pan.
Bake until crisp and browned, about 8 minutes. Remove parchment and prosciutto from pan. Set aside.
Slice larger mushrooms in half lengthwise. On the same pan, combine mushrooms, 5 tablespoons olive oil, 1½ teaspoons salt, and ½ teaspoon pepper, tossing to coat well.
Bake mushrooms, stirring occasionally, until reduced in size, brown, and soft, about 30 to 35 minutes. Transfer mushrooms to a small bowl and set aside.
In a large bowl, toss together spinach, cheese, and walnuts. Tear prosciutto into bite-size pieces and add to spinach mixture. Add mushrooms, tossing to combine.
In a medium skillet, heat remaining ¼ cup oil over medium heat. Add onion and garlic; cook, stirring frequently, until onions are soft, about 8 minutes. Remove from heat and stir in lemon juice, honey, remaining ¼ teaspoon salt, and remaining ¼ teaspoon pepper. Drizzle warm vinaigrette over spinach mixture. Using tongs, toss spinach mixture until well coated with vinaigrette and spinach leaves are lightly wilted. Serve immediately.