Two to three hours before you plan to make this dish, put the puff pastry into the fridge to thaw.
Preheat the oven to 350 degrees Fahrenheit.
In a large stock pot, melt the butter. Add the onions, carrots, and mushrooms. Stir and cook over medium heat for about 5 minutes or until onions are translucent and mushrooms begin to shrink.
Stir in the minced garlic and cook another minute. Add the rutabaga, peas, and celery and stir. Let cook another 2-3 minutes.
Sprinkle flour over the vegetables in the pot and stir to coat. Pour in the vegetable broth and bring to a gentle simmer. Let pot simmer for 7-10 minutes. The liquid in the pot should begin to thicken.
Stir in the oregano, thyme, salt, and pepper. Allow to simmer another 1-2 minutes and turn off the heat.
Arrange 3 or 4 small ramekins onto a baking sheet.
Add flour to countertop or work surface and roll out your puff pastry. You'll need about 1/2 of the package for this recipe. Cut into squared that are the diameter of your ramekins. (Mine were about 5 inches.)
Evenly divide the vegetable filling between each of the ramekins. Top with a sheet of puff pastry. Poke 4 small holes into the middle of the puff pastry to allow steam to escape while cooking.
Bake for 30-35 minutes or until filling is bubbly and the puff pastry is golden brown.