Preheat oven to 400 degrees F.
Cut the chorizo into 1-inch pieces and put them in a food processor. Pulse until the chorizo is finely chopped. Set aside.
Remove the stems from the mushrooms. Mince half the stems (this can be done in the work bowl of the food processor). Reserve the other half of the stems for another use or discard them. Brush the mushroom caps with 1 tablespoon of the olive oil and set on a baking sheet. Set aside.
Pour the remaining 1/3 cup olive oil into a large skillet over medium-high heat. Add the onion and minced mushroom stems. Cook, stirring, just until soft, 2 to 3 minutes. Add the bread crumbs and toss and stir until toasted golden brown. Scrape the bread crumb mixture into a bowl and set aside.
Wipe the skillet clean with paper towels and add the minced chorizo. Cook over high heat until fragrant and glossy, about 3 minutes. Add to the bread crumb mixture. Add the chicken stock and parsley and fluff with a fork. Stir in the Manchego cheese. Use a spoon to fill the mushroom caps, mounding the stuffing attractively. Bake until stuffing is lightly browned, 20 to 25 minutes. Serve hot or warm.
*Cook's Note: Spanish chorizo has a much firmer texture than Mexican chorizo. Cutting it with a knife doesn't really cut it. Pulsing the chorizo in a food processor gives the nice little pieces I'm looking for here.