Carefully remove the stems from the mushroom caps, leaving a hollow well in the mushroom. Transfer the stems to a mini-prep food processor. Roughly chop the shallots and transfer to the food processor with the mushroom stems. Pulse several times until finely chopped.
Line a baking sheet with parchment paper. Place the mushrooms on the parchment - top side down. Drizzle with olive oil and sprinkle lightly with salt and pepper. Set aside.
Heat 2 teaspoons olive oil in a skillet over medium high heat. Add the pancetta and cook for 3-5 minutes or until crispy and golden. Use a slotted spoon to transfer pancetta to stacked paper towels to drain. Set aside.
Add the shallot mushroom stem mixture to the rendered fat in the pan and cook for 3-5 minutes or until softened and fragrant. Stir in the chopped thyme and cook until fragrant, 30 seconds to a minute. Add the chopped spinach and cook until wilted and soft 2-3 minutes. Stir in the whipping cream and simmer for 3-5 minutes until slightly thickened. Remove from heat and add the parmesan and mozzarella, stirring until the cheese melts and the sauce is evenly incorporated. Add 3/4 cup breadcrumbs and the reserved pancetta. Stir to a thick, spoonable consistency.
Spoon filling into the mushroom caps. Sprinkle with the remaining ¼ cup of breadcrumbs. Bake for 25-30 minutes or until mushrooms are softened and filling is soft and bubbly. Transfer to a platter and serve hot.
Notes
Can assemble the mushrooms in advance and bake at the last minute.