Preheat oven to 375.
In a large skillet, heat the olive oil. Add the carrots, leeks and celery, sauté until the carrots start to soften.
Add the mushrooms and cook until softened and darkened, about 5 minutes (add additional olive oil if the pan starts to dry).
Add the peas, broth and stout. Bring to a simmer. Sprinkle with flour, stir to combine. Stir in the oregano, pepper and salt. Cook until thickened, about 2 minutes, remove from heat.
Divide evenly between 6 oven safe (12 to 14 ounce) serving bowls, sprinkle with crumbled goat cheese.
Roll out puff pastry on a lightly floured surface, cut into 6 equal squares.
Top each bowl with one square, press into shape.
Brush with melted butter, slice 3 to 4 small slits in the top of each bowl.
Bake at 375 until puff pastry is golden brown.