PREHEAT broiler to high. REMOVE stems from mushrooms. SCRAPE out gills with a spoon, carefully, so as not to break edges of mushrooms. PLACE mushrooms on foil-lined baking sheet. BRUSH with olive oil; season with salt, pepper and garlic powder. BROIL for 2 to 3 minutes per side or until slightly tender. LET stand until cool enough to handle and remove excess liquid, patting down to dry.
PREHEAT oven to 400°F. PLACE mushrooms cap sides down. BRUSH with mustard and sprinkle with goat cheese.
CRACK egg into each mushroom. SPRINKLE with thyme. BAKE for about 15 minutes or until whites are set and yolks are cooked to desired doneness. GARNISH with chives.
To easily add eggs to mushrooms, crack each egg into a small cup first and then pour into the mushroom.
These mushrooms are also delicious with grated Parmesan cheese or shredded cheddar cheese.