Melt the vegan butter in a large sauce pan over medium heat. Add in the shallots and saute until the rings start to separate, about 3 minutes. Add in the garlic and saute for 2 minutes more. Add in the sliced portobellos, then stir and cover. Reduce the heat to medium-low and allow to simmer for about 5 minutes. Break up the Gardein BBQ skewers and add into the pan, along with the green garbanzos, sliced carrot and dried thyme. Cover again and allow to simmer for about 4 minutes.
Remove the lid, then turn the heat up to high. Once the mixture starts to bubble, add in the wine and reduce the heat back to medium. Next, add in the broth, vegan Worcestershire and soy sauce. Taste the mixture and adjust any seasonings. Add in the arrowroot/water mixture, stir until thickened, then remove the pan from the heat.
Preheat your oven to 400 degrees. Place the some of the mixture into ramekins or any other small oven-safe vessels. Cut the phyllo dough to fit the top of the vessel. Place two sheets on the top and brush with oil. Repeat until 8-10 sheets have been placed on the top. Then place the filled vessels onto a baking sheet and bake for 20-25 minutes, or until the tops are golden brown and bubbly.
Place the leftover filling into the refrigerator. To make additional fresh pot pies with the filling in the following days, just repeat the process described in the paragraph above.