Brush the mushrooms with a damp cloth to remove any dirt, then remove the stems from the mushroom caps. Finely dice the stems but keep the mushroom caps whole.
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 350ºF 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.
Notes
Storage Information: If you have any leftovers you can place them in an airtight container and refrigerate for up to 4 days. Reheat them in the microwave or bake them in the oven at 350ºF for a few minutes. Stuffed mushrooms don't really freeze that well as the texture of the mushroom changes after thawing.