Brush mushroom caps on both sides with oil and season with salt and pepper.
Grill top side down until slightly charred, about 4 minutes. Turn over and repeat for another 3-4 minutes.
Place spinach in bowl and toss with the dressing.
Divide half of the spinach among 4 plates. Top with half of the Manchego cheese and then a mushroom cap. Prepeat the layers in the same order using the remaining spinach and cheese and top with remaining mushroom cap.
Drizzle remaining vinaigrette over the mushrooms and garnish with choped chives.