Preheat oven to 400 degrees F. Line a baking sheet with aluminum foil and brush with oil to grease the foil.
Prepare mushrooms. Use a damp cloth or paper towel to wipe the mushrooms clean. Remove the stems, discarding the tough ones and finely chopping the tender parts. Place mushroom caps with the open side facing up on the prepared baking sheet.
Combine ground pork, garlic, gochujang, brown sugar, soy sauce, mirin, sesame oil, and black pepper in a medium bowl. Mix until well combined.
Heat 1 tablespoon oil in a large saute pan over medium heat. Add seasoned pork and cook until browned, about 4-5 minutes. Add chopped mushroom stems and saute until softened, about 3-4 minutes. Add cream cheese, mozzarella, and salt, stirring until combined. Remove pan from heat and add panko and chives, stirring until well combined.
Spoon pork filling into mushroom caps, pressing it gently so that it fills the cavity, mounding extra on top. Bake stuffed mushrooms for 20-25 minutes or until tenders are tender and tops are browned. Remove from the oven and garnish with chopped chives, if desired. Serve warm.
Notes
You can cook the pork filling the day before, if desired.