Preheat oven to 400°F (200°C). Line a large rimmed baking sheet with parchment paper. Clean mushrooms gently by wiping caps with a damp paper towel. Twist and snap stems off mushrooms; reserve caps and arrange them hollow-side up on the baking sheet.

Finely mince the reserved mushroom stems. Heat 1 tablespoon of olive oil in a skillet over medium heat. Add minced stems and shallots; sauté for 4 to 5 minutes until tender and moisture evaporates. Add minced garlic, thyme, smoked paprika, salt, and black pepper; cook 1 minute until fragrant. Remove from heat and cool slightly.

In a medium mixing bowl, beat softened cream cheese until smooth and creamy. Fold in the sautéed mushroom-garlic mixture, 1/2 cup grated parmesan cheese, and chopped fresh parsley until completely combined.

In a separate small shallow bowl, stir together panko breadcrumbs, 2 tablespoons grated parmesan, and melted butter until crumbs are evenly moistened.

Lightly brush the exterior of mushroom caps with remaining 1 tablespoon olive oil. Spoon a generous rounded tablespoon of garlic herb filling into each cap, mounding the top slightly.

Gently press the stuffed top of each mushroom directly into the panko mixture so crumbs adhere in a thick, uniform crust. Place upright back onto the baking sheet.

Bake at 400°F (200°C) for 18 to 22 minutes, until mushroom caps are tender and juicy, the filling is hot and bubbling, and the panko topping turns deeply golden brown and crisp.

Allow mushrooms to rest for 5 minutes on the baking sheet so the molten cheese filling sets slightly. Transfer to a serving platter, garnish with freshly chopped parsley, and serve warm.