Heat the olive oil in a large skillet over medium-high heat. Add the chopped mushrooms to the hot oil and cook, without stirring, for 2-3 minutes.
Toss the mushrooms with a spatula and season with sea salt and freshly cracked pepper; cook for an additional 2 minutes, then add the minced garlic and a bit of freshly chopped parsley. Cook, stirring continuously for 1 minute, then remove from the heat.
Place a big chunk of brie cheese in each phyllo cup, then top with a spoonful of the mushrooms. Place them on a baking sheet.
Bake in the oven for 4-5 minutes or until the cheese is oozing and the phyllo cups are golden brown.