1. Preheat oven to 375 degrees. Unfold dough onto a lightly floured piece of parchment. Cut into a 10-by-9-inch rectangle (if necessary, roll out slightly first). Trim edges. Transfer dough on parchment to a baking sheet. Use the tip of a sharp knife to score a 1-inch border (do not cut all the way through). Prick center all over with the tines of a fork. Freeze 15 minutes. Carefully brush border with beaten egg (reserve remaining beaten egg for filling). Bake until puffed and golden, about 25 minutes. Remove from oven and press center down to create a hollow.

2. Meanwhile, cut 1/4 inch off of one end of a date. Remove pit. Cut date into 1/4-inch rounds. Repeat with remaining dates.

3. Mix together goat and cream cheeses. Stir in remaining beaten egg, 1/2 teaspoon salt, and 1 teaspoon pepper. Stir in olives. Spread mixture evenly into hollow of tart shell. Toss dates and chiles with oil. Sprinkle over cheese mixture, pressing gently to adhere. Bake until set, about 10 minutes. Drizzle with oil and sprinkle with flaky salt before serving.