Crust:

1. In a food processor, combine flour, salt, and pepper. Pulse three times to combine. Add the butter and pulse until broken down to the size of lima beans. The bigger the pieces of butter, the flakier the dough will be. Mix sour cream and ice water in a liquid measuring cup. Drizzle into the flour mixture gradually, pulsing between additions, until the dough just starts to hold together. Turn out the dough onto a lightly floured surface and shape into a 5-inch disc. Cover with plastic wrap and refrigerate for at least 30 minutes. The dough can be made up to 2 days in advance.

Filling:

1. Preheat the oven to 375°F.

2. In a 2-qt. heavy saucepan combine brown sugar, butter, cream, and corn syrup. Bring to boiling over medium-high heat, stirring to dissolve sugar and melt the butter. Reduce heat to medium. Boil, uncovered, at a moderate steady rate 5 minutes (do not stir). Remove from heat; stir in vanilla and salt. Transfer to a heatproof bowl. Cover; cool 2 hours.

3. On a lightly floured sheet of parchment paper, roll the chilled dough into a 14-inch circle. If the dough is getting too warm, return the baking sheet to the refrigerator for at least 10 minutes. Spread half of the caramel in a 9-inch circle in the center of the dough. Overlap the pineapple slices on top.

4. Take an edge of the crust and fold it over the pineapple. Work your way around the galette, folding up the crust and overlapping as needed, until the pineapple slices have a border all the way around.

5. In a small bowl, whisk together the egg and water. Brush the crust with egg wash and sprinkle with turbinado sugar. Transfer parchment paper with the galette to a baking sheet.

6. Bake until the crust is golden brown, about 50 minutes. Let the galette cool for at least 10 minutes before serving. Drizzle each serving with remaining caramel sauce.