In a large saucepan, combine water and tapioca; let stand 30 minutes. Whisk in almond milk, egg yolks, 1/2 cup sugar, espresso powder and salt. Bring to a boil; reduce heat. Simmer, uncovered, until slightly thickened, 10-15 minutes, stirring frequently. Combine 1/4 cup sugar and baking cocoa; stir into pan. Cook and stir 2 minutes longer.
In a large bowl, beat egg whites on medium speed until foamy. Gradually add remaining 1/2 cup sugar, 1 tablespoon at a time, beating on high after each addition until sugar is dissolved. Continue beating until soft glossy peaks form.
Gently fold a small amount of tapioca mixture into egg whites; return all to pan, whisking constantly. Cook and stir 2 minutes. Remove from heat. Cool 15 minutes; stir in vanilla. Transfer to dessert dishes. Press plastic wrap onto surface of pudding. Refrigerate until cold (pudding will thicken upon cooling).