Make the crust: Whisk the vegetable oil, egg yolk, milk and vinegar in a bowl. Pulse the flour, baking powder, sugar and salt in a food processor to combine; add the butter and pulse until the mixture looks like coarse meal. Add the milk mixture and pulse once or twice, just to moisten the flour.
Transfer the dough to a 9-inch-round tart pan with a removable bottom and pat onto the bottom and up the sides. Cover with plastic wrap and refrigerate until firm, at least 30 minutes. Trim the edges, if necessary.
Preheat the oven to 350 degrees F. Pierce the dough all over with a fork. Line with foil and fill with pie weights or dried beans. Place the pan on a baking sheet and bake 15 minutes. Remove the foil and weights; continue to bake until golden, 10 to 15 more minutes. Beat the whole egg with 1 teaspoon water, then lightly brush over the crust and bake 5 more minutes. Cool completely on a rack.
Meanwhile, make the filling: Sprinkle the gelatin over 1 tablespoon cold water in a bowl and let soften 5 minutes. Put the granulated sugar and vanilla seeds in a saucepan and rub the seeds into the sugar with your fingers. Add 1 cup cream and whisk over medium heat to dissolve the sugar. When the mixture comes to a boil, remove from the heat and whisk in the gelatin mixture. Transfer to a bowl, then set in a larger bowl of ice water and stir with a rubber spatula until the mixture begins to thicken. Add the remaining 1/4 cup cream and stir until thick, about 2 minutes. Pour into the tart shell and refrigerate until set, about 1 hour.
Before serving, top the tart with the strawberries and confectioners' sugar.