Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper and set it aside.
Put the mushrooms in a food processor or blender and pulse until they form a very smooth puree.
Crush the buttery crackers into fine crumbs using a rolling pin or the food processor, then set the crumbs aside.
Cut the cheddar into small cubes and reserve for stuffing; you can use one to three cubes per bite depending on how cheesy you want them.
In a large bowl combine the ground beef, pureed mushrooms, crushed cracker crumbs, mustard, ketchup, Worcestershire sauce, black pepper, onion powder, garlic powder, and the cracked egg.
Mix everything together using clean hands until the ingredients are evenly incorporated, taking care not to overwork the meat.
Portion the mixture into 12 equal pieces. Press each portion into a shallow indentation, place the cheese cubes inside, then fold and shape the meat around the cheese to form sealed balls.
Place the stuffed meatballs on the prepared baking sheet, spacing them slightly apart so they cook evenly.
Bake for about 30 minutes, or until the meatballs are cooked through and reach an internal temperature of 160°F (71°C). Let them rest briefly before serving.
Serve warm on their own, alongside mashed potatoes, or with your favorite sauce for dipping.