Preheat oven to 350ºF.
Combine olive oil and vinegar and brush both sides of the mushroom caps.
Line a rimmed baking sheet with parchment paper, and add the portobello mushrooms with the opening up.
Melt the butter in a small skillet and add onion, cook for 2 minutes, then add garlic. Cook and stir for a minute, then added the chorizo. Cook and break up chorizo into small pieces. Once sausage is browned, mix in the riced cauliflower and stir to combine. Add salt and pepper to taste.
Remove the sausage mixture from the heat and spoon the sausage mixture into the portobello mushrooms.
Top each portobello with grated cheese and bake the stuffed mushrooms until mushrooms are done, about 10-15 minutes depending on the thickness of the mushrooms. Top with fresh parsley and serve hot.