In a medium bowl, lightly beat ground flaxseeds (flax meal) with warm espresso with a fork. Set aside.
In a medium saucepan, combine 1 1/2 cups milk, 1/3 cup sugar and salt. Bring to a simmer over medium heat, stirring occasionally.
Meanwhile, in a medium bowl whisk the remaining 1/3 cup sugar, cocoa powder and cornstarch. Then whisk in the remaining 3/4 cup milk until blended. Whisk the simmering milk mixture into the cocoa mixture.
Pour the mixture back into the saucepan and bring it to a simmer over medium heat, whisking constantly, until thickened and glossy, about 3 minutes. Remove from heat.
Whisk about 1 cup of the hot cocoa mixture into the beaten flaxseeds. Add this mixture to the saucepan and cook over medium-low heat, whisking constantly, until steaming and thickened, about 2 minutes. Do not let the mixture boil. Whisk in vanilla. Serve warm.