Heat the oil in a saucepan. Add the onions, carrots and celery along with a dash of salt and ground black pepper. Sweat the vegetables until the onions are translucent. You don't want to brown them.
Add the garlic, saute a few seconds, then add the potatoes, rosemary and thyme. Mix well.
Add the all purpose flour and saute for a couple of minutes, stirring constantly. Add in the entire bottle of Guinness. Alcohol is highly flammable, so when adding it to anything that's on the stove, make sure you either turn your flame off, or reduce it really low so it doesn't catch any spatter.
Stir the stew and let it bubble away for a couple of minutes. It will look really thick at this stage because of the all purpose roux, but that's fine.
Add the tomatoes and let the stew continue to cook, covered, for about 10 minutes. You want to let the potatoes get tender and you want the bitterness of the Guinness to dissipate to your liking. The more you let the stew cook, the more you'll cook out the alcohol.
Add the chick'n pieces to the pot and, if needed, add some of the vegetable stock to thin out your stew. You can make this as thick or thin as you want. I prefer my pot pie filling really thick, so I used less.
Check to see if you need more salt and ground black pepper, and turn off the heat after the stew comes to a boil. Stir in the vegan butter and the basil.
Preheat the oven to 400 degrees Fahrenheit.
To assemble your Guinness pie, pour the stew into a two quart baking dish (a deep-dish pie plate works too)
Cut the puff pastry sheet into strips with a pastry cutter or pizza cutter. Depending on the width or diameter of your baking dish, you may need to roll out the puff pastry a little to fit. Now layer on the strips over the stew, as nicely as you can, forming a lattice top. Trim any overhanging edges. Or, if you'd rather not do this, just place the puff pastry sheet over the stew and cut a few slits in the middle, as you would for a pie.
Place the Guinness Pie in the oven and bake 30 minutes or until the puff pastry is all golden and the stew is bubbling around the edges.
Remove from the oven and serve hot.