Preheat the oven to 350 degrees. Grease a rimmed baking sheet with a little olive oil.
Wash the mushrooms and remove the stems. Place them on the baking sheet and bake at 350 degrees for about 30 minutes.
While the mushrooms bake, boil the potatoes until tender, about 20 minutes.
Drain the potatoes, then add the vegan buttery spread, coconut milk, and spices. Use a potato masher or a hand blender to mix until smooth and creamy. Add the spinach and stir until heated through.
Remove the mushrooms from the oven and drain off the excess juice from each mushroom cap. Set the oven to 450 degrees.
Fill each mushroom cap with the potato mixture. You may not use all the potato mixture depending on how large the mushrooms are.
Place the filled mushrooms back in the oven for about 5 minutes to heat them through.
Let cool for a minute before moving the mushrooms to a serving tray.