Mix together the coconut milk and corn starch and set aside.
Heat the coconut oil in a pan over medium high heat. When it's hot, add the mushrooms and garlic. Sauté the mushrooms for about 5 minutes until they soften and begin to release their juices. Stir in the coconut milk mixture, nutritional yeast, thyme, oregano, salt and pepper. Reduce heat to a simmer. Continue to cook for about another 5 minutes, until the sauce thickens a bit. Remove from heat.
Lightly flour a clean work surface and use a rolling pin to roll out the puff pastry to a rectangle that's about 9" x 12". Use a long knife to cut the puff pastry into 24 squares. that's 3 cuts down the longest direction, and 5 cuts across the shortest direction.
Push each puff pastry square into the mini cupcake pan, so that the edges of the puff pastry, come up the sides forming a little cup to hold the mushroom mixture. If any of your squares are a little too small, just use your rolling pin to roll it out a little more. Divide the mushroom mixture evenly among the cups.
Bake for 25 - 30 minutes, rotating the pan once until the edges of the puff pastry are golden. To remove them, use a knife to pop them out of the pan. Finely chop chives, cilantro, or parsley, and sprinkle on the mushroom puffs for garnish.
*If you like, you can make the mushroom mixture ahead of time and store in an airtight container until you are ready to full the puff pastry. *You will need a rolling pin which you can purchase here, and a mini cupcake pan which you can purchase here.