Dulce de Leche Torte (Volador)

Preheat oven to 400°F with rack in middle. Generously brush a large baking sheet with vegetable oil.
Stir together yolks, milk, and salt.
Put flour in a large bowl and make a well in center. Add yolk mixture to well and gently stir with a fork, gradually pulling in flour closest to egg mixture to make a paste. Knead in all of remaining flour with your hands to form a dough (dough will be very firm).
Transfer dough to a work surface and knead, lightly dusting with additional flour as necessary, until smooth and elastic, 8 to 10 minutes.
Flatten dough into a disk, then quarter and form each quarter into a ball.
Keeping remaining dough covered with a kitchen towel (not terry cloth), firmly roll out 1 piece on a clean surface into a 12-inch round, lifting and turning dough as necessary. (Dough will be slightly sticky but will lift up easily; round will be very thin with uneven edges.)
Transfer to baking sheet and bake until edge is golden and curls up, about 5 minutes. Carefully turn over and bake until cooked through and both sides are golden in some spots (lift to check), 3 to 4 minutes more. Transfer to a rack to cool.
Repeat with remaining dough. (Pastry will overlap on racks.)
Stir together dulce de leche and water in a bowl. If mixture is not spreadable, warm in a small heavy saucepan over medium-low heat, whisking until smooth. Thin with additional water if necessary.
Arrange 1 pastry layer on a serving plate and spread evenly with 2/3 cup filling. Repeat with 2 more pastry layers and remaining filling, stacking layers.
Dust remaining pastry layer with confectioners sugar and arrange on top.
To serve, cut or crack torte into portions using 2 large spoons.