Preheat oven to 350°F. Line the base of an 8-inch round springform pan with parchment paper.
To make the crust, blend together flour, cocoa powder, brown sugar and salt in a medium bowl so there are no lumps of brown sugar. Stir in melted butter and use your fingertips to combine all ingredients so it forms damp crumbs. Turn the crumbly mixture out into prepared pan and press it down in an even layer, pushing it about ¾-inch up the sides to form an edge. Run the back of a spoon across the surface to smooth it out. Bake for 12-15 minutes until slightly puffed and feels dry to the touch. Transfer to a wire rack.
Reduce oven temperature to 300°F.
To make the filling, beat cream cheese using a hand mixer in a large bowl until smooth. Add sugar and vanilla and beat until silky and glossy (you can also use a food processor). Beat in eggs one at a time and then mix in sour cream until evenly blended. Gently mix in melted chocolate until it is evenly incorporated and then mix in hot water until it is smooth.
Pour the filling over the pre-baked crust and smooth out the surface. Bake for 45 minutes until set around the edges and slightly wobbly in the center. Turn off the oven and leave it in for another 10 minutes. This gentle cooking produces the silkiest texture. Transfer to a wire rack to cool completely and then refrigerate for at least 2 hours.
To make the glaze, combine water and chopped chocolate in a small saucepan over medium-low heat and whisk until completely melted, smooth and silky. Remove from heat and let cool for 10 minutes, then pour the glaze over chilled cheesecake and spread it out evenly. Refrigerate until set and then top with dark chocolate curls. Slice with a hot dry knife.
TIP: Even though I have success with this recipe without a water bath, you can still use one to absolutely ensure an extra creamy texture and to guard against cracking. Wrap the base of the round baking pan with a double layer of aluminum foil. Place it onto a rimmed baking tray. Pour boiling water into the baking tray so that it comes about ½-inch up the sides of the foil-wrapped pan and bake as directed.