Wash and trim the mushrooms. Lightly brush 1 Tbsp. of melted butter or olive oil inside the mushrooms. Next, season with pepper. (I season with salt at the end.)
Place mushrooms on a lined baking sheet. Bake for 15-20 minutes.
Meanwhile, in a large skillet, brown the ground pork over medium heat. Then, add 1 Tbsp. of butter or olive oil. Once melted, stir in the flour. Allow to cook for 2-3 minutes. Next, stir in the milk/cream. Bring to a boil. Then, lower the heat and simmer for minutes, until mixture thickens enough to coat the back of a spoon.
Spoon the sausage gravy into each mushroom cap. Sprinkle with cheese. Broil just until cheese melts, about 2 minutes. If desired, season with salt.