In a large bowl, combine the flour, sugar, baking powder, and salt. Add the butter and cut it into the dough using two knives, a pastry blender, or your fingertips until the dough looks crumbly. Add the egg and 1 tablespoon water; mix with a fork until the dough just holds together. (If the dough won't come together, add up to another 1-1/2 teaspoons water, a tiny bit at a time.) Don't overmix; the dough should feel slightly sticky. Shape the dough into a 6-inch log. Wrap it in plastic and refrigerate until firm, about 1 hour.

Heat the oven to 400 degrees F. Cut the chilled dough into six equal pieces. Roll each piece into a round about 1/8 inch thick. Prick the rounds all over with a fork and gently fit them into 4-inch tartlet pans, trimming any excess dough.

Line each tartlet with foil and fill with dried beans or pie weights. Bake the tartlet shells for about 15 minutes. Remove the pie weights and the foil and bake an additional 5 minutes until golden. Cool on a rack.

Heat the oven to 350 degrees F. Combine the toasted nuts, coconut, and raisins with the warm butterscotch sauce. Divide the filling among the six tartlet shells. Bake until the filling just starts to bubble, 7 to 9 minutes. Using a wide spatula, carefully transfer the tartlets to a rack. Allow the tartlets to cool for 5 minutes. Carefully remove the tartlets from their pans and serve warm with a dollop of unsweetened whipped cream or creme fraiche, if you like.

In a medium, heavy-based saucepan, melt the butter. Stir in the two sugars, the salt, water, and corn syrup. Bring the mixture to a boil over medium-high heat, stirring to dissolve the sugars. Let the mixture boil for 5 minutes, stirring often. You'll see big, slow bubbles as it boils. Remove the sauce from the heat. Carefully whisk in the cream and vanilla (the sauce may sputter). Allow the sauce to cool to warm before serving.

Make Ahead: Refrigerated, this sauce will keep for about two weeks. Reheat it gently, adding a little cream if it's too thick.