Make the pie crust first. Sift the flour into a large mixing bowl, then pour in the salt and stir to combine.
Then break the cold vegan butter up into small pieces and drop them all over the flour. Using your fingers or a fork, press and pinch the butter until it is evenly distributed in the flour and the flour resembles sand or dirt texture.
Now, pour the ice cold water into the bowl, a little at a time, stirring until it gets too hard to stir, then begin to knead with your hands until you form a nice smooth ball. Cover the pie dough and place in the fridge while you make the filling.
Heat the olive oil on medium high in a large pot. Then add the garlic and onion. Saute for 2-3 minutes or until the onion starts to become translucent.
Then add the potatoes and carrots to the pot. Season with a few pinches of salt and pepper. Saute for about 10 minutes to start softening the potatoes.
Next, add all of the mushrooms. Toss with the other veggies and continue to saute for about 10 more minutes. The mushrooms should release their liquid and begin to brown. Season with another pinch of salt and pepper.
Add the tomato paste and stir to coat the veggies with the paste.
Now, pour the beer into the pot and scrap any brown bits that are stuck to the bottom.
Add the vegetable broth, soy sauce, thyme, rosemary and a pinch of salt and pepper.
Stir and reduce heat to medium low, simmer for 5-7 minutes or until the potatoes are tender.
In a small bowl, whisk the corn starch and water together, and then add that to the pot. Stir to combine and simmer the filling for another 2-3 minutes or until it thickens slightly.
Remove the sprig of thyme and rosemary, then taste and adjust seasonings. Remove from heat.
Preheat the oven to 400 degrees(F).
Take the pie crust out of the fridge, if it it too firm to roll out, let it sit on the counter for a few minutes while the oven preheats to soften it a bit.
Take 4 medium sized ramekins or small baking dishes, and divided the stout and vegetable filling evenly into the dishes.
Then roll out the pie crust on a floured surface, roll it to about an 1/8 inch thick. Then cut 4 circles out that are slightly larger than the baking dishes.
Place each circle over the filling in the baking dishes and press the crust down around the sides of the dish to seal it. Pierce the top of the crust with a knife a few times to let out the steam. Then brush the tops of the crusts with the oil.
Place all the dishes on a baking sheet and bake for 10-15 minutes or until the crust is golden brown and baked through. Serve!