Remove the stems from the mushrooms and finely chop enough to fill 1 cup. Set aside.
Spray a large nonstick skillet with the butter-flavored cooking spray. Preheat over medium heat.
Add the sausage to the skillet and stir, while browning, to crumble. Add the chopped mushroom stems, onions, thyme, black pepper, and 1 tablespoon of broth. Cover the skillet and cook for about 3 minutes, stirring frequently, until the vegetables are tender. If the skillet becomes dry during cooking add a little more broth.
Allow the skillet to cool slightly for a few minutes. Toss the breadcrumbs into the skillet mixture to mix. Add the remaining broth slowly, tossing gently to mix. The texture of the mixture should be moist but not wet. If needed, toss in more broth.
Spray a 9x13-inch pan with the cooking spray. Spoon 1 tablespoon of the stuffing into each mushroom cap. Press the stuffing gently to help it hold together. Place the mushrooms in the pan and spray their tops lightly with the cooking spray.
Cover the pan with aluminum foil and bake for 12 minutes. Remove the foil and bake for 5 minutes until the mushrooms are tender and the stuffing is browned.