Brush mushrooms with olive oil and sprinkle with salt and pepper. Place face up on a baking sheet and roast for 15 minutes. Pour out any liquid that accumulated in the caps. Set aside.
Spray a medium skillet with cooking spray. Over medium heat, cook spinach until wilted, about two minutes. Divide cooked spinach evenly between the mushroom caps.
Whisk eggs, milk, cheese, salt and pepper together. Pour egg mixture into the skillet and cook over medium heat, stirring frequently, until eggs are cooked through. Divide scrambled eggs between the mushrooms. Place the assembled mushrooms back in the oven for 3-4 minutes, just to heat the mushrooms. Sprinkle with chives and serve immediately.