1. Heat oven to 325°F. Place oven rack at position just below center. You'll need a 10-in. tube pan with removable bottom. Whisk flour, 3/4 cup sugar, baking powder and salt in a large bowl.
2. Stir cocoa and espresso with boiling water in a medium bowl until dissolved; add cold water, oil, yolks, liqueur and vanilla. Stir cocoa mixture into flour mixture until blended.
3. Beat whites and cream of tartar in a large bowl with mixer on medium-high speed until soft peaks form when beaters are lifted. Gradually beat in remaining 1/2 cup sugar. Beat until glossy and stiff peaks form.
4. Stir 1/4 of beaten whites into cocoa-flour batter to lighten. Gently fold batter into rest of whites until no white streaks remain. Pour into ungreased pan.
5. Bake 1 hour or until wooden skewer inserted into center comes out clean. Invert pan onto neck of a tall, narrow bottle, such as a wine bottle; cool completely. Run a thin knife around sides of cake; remove pan sides. Repeat with bottom of cake. Invert onto cake plate. Remove pan.
6. Glaze: Melt chocolate in microwave on high about 1 minute, stirring every 15 seconds. Whisk in half-and-half. Pour glaze over cake, spreading top with spatula. Sprinkle with hazelnuts.