Remove phyllo dough from package and cover with a dry towel. Using a pastry brush, spread olive oil on 1sheet of dough. Place another sheet on top and brush with more oil. Repeat 3 more times to finish with 5 layers. Cut the dough into 4 equal squares. Place each square on an inverted ramekin on a sheet pan. Bake at 400 degrees for approximately 5 to 8 minutes or until golden brown.
Make the vinaigrette by simply mixing all of the ingredients in a mixing bowl.
Cut the 8 ounces of goat cheese into 4 equal parts. Place the goat cheese into the phyllo "cup" and put in a 300 degree oven for about 2 minutes. Remove from oven and place onto a plate. Toss the greens with the vinaigrette and place on top the cheese. Serve immediately.