Trim off root end of leeks. Cut off all but 1" of the dark green leaves and discard. Cut leeks in quarters lengthwise, then cut in 1 1/2" pieces. Put leeks in a large bowl of water to wash off grit. Change water and rinse again until clean. Drain and pat dry.
Melt butter in a skillet. When foam subsides and butter is just beginning to brown, add leeks. Season with salt and pepper, and saute 2 minutes until tender. Transfer to a sheet pan and refrigerate 10 minutes until cool.
Crack 8 eggs into a bowl and beat lightly. Add milk, cream and goat cheese, and whisk together. Add worcestershire and tabasco.
Grease a pie dish with butter. Place leeks in bottom of dish. Pour custard base over leeks. Place pie dish on a baking sheet. Place in preheated 400°F oven for 15 minutes.
Lay sliced brie over top of dish. Return to oven for another 10 minutes. Cool 3 minutes before slicing and serving.