For Pate Choux: Place water, butter, sugar, and salt in a saucepan. Bring to a gentle boil. Remove from heat, add flour, stir with a wooden spoon until it forms a solid dough ball. Return to medium heat and cook gently for 2 minutes. Remove from heat and transfer to a mixer bowl - fitted with a paddle. Beat at medium speed until dough has cooled. With the mixer running add each egg separately, until it forms a loose dough (thicker than cake batter, thinner than biscuit dough.) Immediately transfer to a piping bag fitted with a round tip. Pipe dough in 2" logs, about 1" apart on parchment paper lined baking sheet. Brush lightly with egg wash and bake at 425 degrees until golden brown (approximately 12 minutes.) Turn off the oven, and let them dry out for about 30 minutes. Cool completely.
PASTRY CREAM: Place the milk and vanilla bean into a saucepan and bring to a boil. Whisk the yolks together with sugar until light and frothy, (light yellow). Stir in the sifted cornstarch until combined. "Temper" the hot milk into the egg mixture. Return to medium heat and stir in 2 Tbs. butter. Place in bowl and cover with plastic wrap directly on the mixture to prevent it from forming a skin. When cool - put it in a pastry bag with a very small round tip.
TO ASSEMBLE: Poke a tiny hole in one end of the eclair. Gently fill with pastry cream.
TOPPING: Melt chocolate and carefully dip the top of eclair halfway into the chocolate. Allow it to dry and harden on a baking sheet. Melt white chocolate - put in a ziploc bag or a small piping bag fitted with a tiny round tip. Drizzle white chocolate over the hardened chocolate - and allow it to harden.