How to Make It
Stem the Portobellos and cut the caps in half. Using a sharp paring knife, cut off the black gills from the undersides of the caps. Slice the caps crosswise 1/4-inch thick.
Melt the stick of butter in a large skillet. Add the shallot and cook over low heat until softened, about 4 minutes. Stir in the Portobello and white button mushrooms and season with salt and pepper. Cook over moderate heat, stirring occasionally, until the mushrooms are tender and their liquid has evaporated, about 10 minutes. Stir in the garlic, parsley and thyme and cook for 2 minutes longer, stirring. Transfer the mushroom mixture to a food processor and pulse to a coarse puree. Scrape the puree into a medium bowl, stir in the goat cheese and season with salt and pepper. Let cool.
Preheat the oven to 400$#176;. Lay 1 sheet of the phyllo dough on a work surface; keep the rest covered with damp paper towels. Brush the phyllo sheet with melted butter and cut it lengthwise into 4 even strips. Place 1 level tablespoon of the mushroom filling in a corner of one of the strips, about 1/2 inch from the top. Fold the corner down to form a triangle. Continue folding the triangle onto itself, across and down, until you have a neat phyllo triangle. Set the triangle on a large rimmed baking sheet. Repeat with the remaining phyllo, melted butter and mushroom filling. Brush the triangles with melted butter and bake for about 20 minutes, or until browned and crisp. Let cool slightly before serving.