For the cake: Preheat oven to 375 degrees. Coat an 8-inch round cake pan with spray.
Whisk water and cocoa in a small bowl until smooth. Combine flour, sugar, baking soda, and salt in a large bowl, and make a well in center. Add cocoa mixture, oil, and vanilla. Whisk until smooth. Whisk in vinegar. Pour into pan.
Bake until a toothpick inserted into center comes out clean, 30 to 35 minutes. Let cool on a wire rack for 20 minutes. Run a knife around edge of cake, invert it onto rack, and turn cake right side up. Let cool completely. Transfer cake to a serving plate or a cake stand.
For the glaze: Melt chocolate in a heatproof bowl set over simmering water, stirring until smooth. Let cool slightly.
Whisk together sugar and water until smooth. Add melted chocolate in a slow, steady stream, whisking until thickened, about 1 minute. Immediately pour glaze onto center of cooled cake. Using an offset spatula, gently spread glaze over top and sides. Cake can be stored at room temperature for up to 2 days.