Combine first 2 ingredients in a small saucepan. Bring to a boil; boil 1 minute, stirring occasionally. Remove from heat; stir in liqueur.
Combine 1 3/4 cups milk and eggs in a large bowl, stirring with a whisk. Add espresso mixture, stirring with whisk. Add bread, stirring to coat. Pour bread mixture into a 2 1/2-quart round casserole coated with cooking spray. Place dish in an oval 7-quart electric slow cooker. Cover and cook on LOW for 2 hours or until set.
Combine remaining 1/4 cup milk, mascarpone cheese, and vanilla in a small bowl, stirring with a whisk until smooth. Spoon bread pudding into dessert dishes; top each with mascarpone sauce, and sprinkle with cocoa.