How to Make It
Heat 1 tablespoon of the oil in a large skillet. Add the onion and cook over moderately low heat, stirring, until softened, about 10 minutes. Add the garlic and cook until fragrant, about 1 minute. Add the tomato and cook, stirring occasionally, until the liquid is evaporated and the sauce is thick, 7 to 8 minutes.
Transfer the sauce to a bowl and wipe out the skillet. Add 1/2 tablespoon of the oil and heat until shimmering. Add the pork in small clumps and cook over moderately high heat until browned, 8 to 10 minutes. Add the tomato sauce along with the chicken stock, tomato paste and fennel seeds and cook over low heat until thickened, about 5 minutes. Season the picadillo with salt and pepper and transfer to a plate.
Preheat the oven to 350°. Using a melon baller or small spoon, scrape out the brown gills from the mushroom caps. Wipe out the skillet again and heat the remaining 1 1/2 tablespoons of olive oil until shimmering. Add the mushrooms, top side down, and cook over moderately high heat until golden brown, about 2 minutes. Turn the mushrooms and cook until brown on the other side, about 2 minutes longer.
Transfer the mushroom caps to a medium baking dish and fill them with the picadillo. Bake the mushrooms for about 15 minutes, or until cooked through. Transfer the mushrooms to a platter or individual plates and serve.