Gently clean the mushroom caps with a damp paper towel. Use a spoon to remove the stem and gills from the underside of the mushrooms.
Spray mushroom caps with olive spray on both sides. Sprinkle liberally with salt and pepper. Place the mushrooms stem-side up on a baking sheet.
Heat 1 tbsp olive oil in a large, non-stick pan over medium heat. Add onion and cook for 3-4 minutes, until softened. Add roasted red peppers, garlic, oregano, and dill. Cook for 2-3 minutes. Add the spinach and cook until wilted, about 2-3 more minutes. Stir in breadcrumbs and vegan feta cheese (if using). Cook for 1-2 minutes until heated through, and remove from heat.
Spoon the filling into the four mushroom caps. Bake for 20-25 minutes, until mushrooms are softened and slightly browned.