1. Preheat oven to 425°.
2. Heat oil in a skillet over medium-high heat. Add onion, thyme, salt, and pepper; cook 20 minutes, stirring occasionally.
3. Roll dough out on a parchment paper-lined baking sheet. Sprinkle feta cheese in center, leaving a 1 1/2-inch border; top with onion. Sprinkle with Swiss cheese. Fold piecrust border up and over onion mixture, pleating as you go, leaving a 6-inch-wide opening. Combine egg and 2 tablespoons water; brush over dough. Bake at 425° for 25 minutes or until golden. Cool for 10 minutes.