Preheat oven to 375 degrees F. Twist or cut off stems from mushrooms. Chop stems; set aside. Use a spoon or sharp knife to scrape out the gills from mushroom caps; discard gills. Brush 1 Tbsp. of the dressing onto rounded sides of mushroom caps; place, rounded sides down, in foil-lined 15x10x1-inch baking pan.
Heat remaining 3 Tbsp. dressing in Dutch oven on medium-high heat. Add mushroom stems, red pepper and garlic; cook and stir 2 min. Add spinach. Reduce heat to medium-low; cover and simmer 4 min. or until spinach is wilted, stirring after 2 min. Spoon evenly over mushroom caps; sprinkle with cheese.