Line an 8- x 12-inch glass baking pan with heavy-duty plastic wrap or parchment paper, allowing plastic to extend 1 inch over sides of pan. Brush with canola oil.
Combine instant espresso and 3/4 cup cold water in a bowl. Sprinkle gelatin over mixture; set aside.
Combine remaining 1/2 cup water, sugar, corn syrup, and salt in a large heavy saucepan. Cook over low heat, stirring until sugar dissolves. If necessary, wash down sides of pan with a wet pastry brush to dissolve any sugar crystals clinging to side of pan. Cook syrup, without stirring, until a candy thermometer registers 240°. Remove from heat.
Pour syrup carefully into softened gelatin mixture, mixing on low speed with an electric mixer. Increase speed to high; beat mixture about 12 minutes or until mixture is very thick and pale. Beat in vanilla.
Pour mixture into prepared pan. Dust top lightly with powdered sugar, and refrigerate. Cut cooled marshmallows into squares using an oiled knife. Toss marshmallows in powdered sugar to coat all sides. Marshmallows will store up to two weeks in an airtight container.