In a large bowl, stir together sugar, butter, and vanilla extract. Add eggs and mix to combine. Add the flour mixture 1/3 at a time to the butter/egg mixture and stir until just combined.
1 cup Sugar, 1/2 cup Butter, 1 1/2 tsp Vanilla extract, 3 Eggs
Dampen your hands and shape dough into 2 4"x10" logs on a parchment-lined baking sheet. Beat the egg with the teaspoon of water. Brush on the egg wash.
Reduce the heat to 300F.
Bake about 30-35 minutes until lightly golden. Transfer the baking pan to a wire rack and cool for 10-15 minutes, cool enough to handle.
Using a very sharp, serrated knife, cut the logs into 3/4-inch slices and arrange on the baking sheet, cut side down.
Bake biscotti again for 25-30 minutes.
Transfer to a wire rack to cool completely.
Notes
Keep in an airtight container at room temp for up to 2 weeks or freeze for up to 3 months.