Start by prepping the mushrooms. Using a damp paper towel, wipe down any dirty mushroom caps. Remove shiitake stems, and slice the caps. Trim cremini stems, and slice. Trim the bottom of the maitakes, then tear into bite-sized pieces. Tear chanterelles into bite-sized pieces.
Add 1 tablespoon canola oil to an 8-inch cast-iron skillet over medium-high heat. Once the oil is hot, add the mushrooms, tossing to coat in the oil. Cook until the mushrooms are tender and golden (about 6 to 8 minutes). Don’t move the mushrooms around too much as they are cooking, so they can develop a nice golden sear. Season to taste with a pinch or two of salt, then transfer to a bowl.
Add chorizo to the same skillet and return to medium heat. Cook, stirring to break up the meat, until firm and crumbly (about 8 minutes). Transfer to a bowl.
Preheat an oven to 425°F. Add 1 tablespoon canola oil to the same skillet over medium heat. Once the oil is hot, add onion with a pinch of salt, and cook until soft and just starting to brown (about 5 minutes). Stir in garlic, cooking just until fragrant (about 1 minute). Stir in grated cheese, then transfer the skillet to the oven. Bake until the cheese gets all melty, and the surface develops golden brown spots (10 – 15 minutes).
* I used a mix of chanterelle, cremini, shittake and maitake mushrooms here. Use whatever wild mushrooms are available at your market. Just creminis would be fine here. The only mushroom I wouldn’t use is white button. They’re better raw.