Combine 1 cup flour, sugar, undissolved yeast and salt in a large bowl. Heat milk, water and butter until very warm (120° to 130°F). Beat 2 minutes at medium speed of an electric mixer, scraping bowl occasionally. Add eggs, vanilla and 1 cup flour; beat 2 minutes at high speed. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
Divide dough into 3 equal pieces; roll each piece to 18 x 6-inch rectangle. Spread 1/3 of the Almond Filling over each rectangle, leaving 1/2-inch border. Starting at long side, roll up tightly as for jelly roll. Pinch seam and ends to seal. Braid the 3 dough rolls; pinch ends and tuck under to seal. Place on greased baking sheet. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Combine egg white and water; brush over braid. Bake in preheated 350°F oven for 30 to 35 minutes or until done.
Remove from baking sheet; cool on wire rack. Drizzle with Almond Glaze; sprinkle with almond slices.
Almond Filling: Combine almonds, sugar, butter, almond extract, vanilla and egg in a medium bowl. Stir to blend.
Almond Glaze: Combine powdered sugar, almond extract and enough milk to reach desired consistency.