Preheat oven to 180°C. Heat half the olive oil in a large skillet or cast-iron pan over medium heat. Add the shallots and sauté for 10 minutes or until softened and starting to brown.
Stir in the garlic and thyme then sauté for a further two minutes or until fragrant. Pour in the stock and deglaze the pan.
Bring to a boil then reduce heat, add the rice, nutritional yeast and simmer stirring regularly for 25 minutes or until liquid is absorbed. Remove from heat and season to taste.
Meanwhile, thoroughly clean the mushrooms then remove the stems. Brush the outside of the mushroom with remaining olive oil then place onto a lined baking tray. Transfer to oven and bake for 10 minutes or until slightly softened.
Remove mushrooms from oven and begin spooning equal portions of rice mixture into each mushroom. Top the stuffing with a light sprinkling of breadcrumbs. Return to the oven and bake for 15 minutes or until golden brown on top. Serve immediately.