Liberally spray a baking sheet with non stick cooking spray.

Put granulated sugar, corn syrup, salt, and 3/4 cup water into a medium saucepan. Bring to a boil over high heat, stirring to dissolve sugar. Cook, without stirring, until mixture registers 238 degrees on a candy thermometer, about 9 minutes.

Meanwhile, put 3/4 cup cold water into the bowl of an electric mixer; sprinkle with gelatin. Let soften 5 minutes.

Attach bowl with gelatin to mixer fitted with the whisk attachment. With mixer on low speed, beat hot syrup into gelatin mixture. Gradually raise speed to high; beat until mixture is very stiff, about 12 minutes. Beat in vanilla. Quickly pour half into prepared baking sheet, swirl with dulce de leche and top with remaining. Smooth top with an offset spatula. Set aside, uncovered, until firm, about 3 hours.

Sift 1 cup confectioners' sugar onto a work surface. Unmold marshmallow onto confectioners' sugar. Lightly brush a sharp knife with oil, then cut marshmallow into 2-inch squares. Sift remaining 1/2 cup confectioners' sugar into a small bowl, and roll each marshmallow in the sugar to coat. Marshmallows can be stored in an airtight container up to 3 days.