Wash the mushrooms and remove the stems, then finely dice the stems.
In a medium skillet over medium heat, melt the butter. Add the diced mushroom stems and garlic, and saute until tender and fragrant, about 3 minutes.
Stir in the sage and season with salt and pepper. Saute one more minute, then remove from heat and let cool 5 minutes.
Preheat the oven to 350F and grease a large glass or ceramic baking dish.
In a large bowl, combine the cream cheese, grated cheddar, and sautéed mushroom mixture. Use a rubber spatula to mix well.
Spoon the mixture into the mushroom caps, pressing in to fill the whole cavity. Place in the prepared baking dish and bake until the cheese is bubbling and melted, and the mushrooms are tender, 15 to 20 minutes.
Remove and let cool 10 minutes, then sprinkle with chopped sage before serving.