Preheat the oven to 350 degrees F. Set out a 9x13-inch baking dish. Gently pop off the stems of the mushrooms. Discard the stems or save for later use. Then use a damp paper towel to brush off the dirt on the mushroom tops. Do rinse them in water.
In a medium bowl, mix the cream cheese, smoked cheddar cheese, diced red pepper, onion, and garlic together. Add 1/4 teaspoon salt and 1/4 teaspoon ground black pepper. Mix well.
Use a spoon to pack the cavity of each mushroom with cheese filling. It's ok if it pops over the top a little.
Press each cheese-stuffed top in grated Parmesan cheese to create a crust. Then set them in the baking dish, cheese-side-up. (It's okay if they are tightly fitted in the baking dish, because they will shrink while baking.)
Bake for 30-35 minutes, until the tops are puffed and golden. Serve warm.
This is a great party appetizer to prep a day or two ahead, then bake right before your event.