For the crust: In the bowl of a food processor combine both flours, salt, and butter and pulse the processor to roughly distribute the butter – approximately 6 times.
While the machine is running, drop the shortening into the bowl. Immediately pour in the water. Pulse 3 or 4 times. Do not overmix. The dough should be rough but able to make a ball.
Turn the dough onto a work surface. Using the heel of your hand, blend the pastry dough until smooth. Reform a ball after each time you mash it down. Repeat until the dough is smooth and blended – approximately 6 times. Form the dough into a disc. Wrap in plastic and chill for at least 2 hours.
For the filling: Cook bacon in a skillet over medium heat until about three-fourths cooked. The fat should not be white and the bacon should not be crispy. Drain on a paper towel and reserve. Wipe the skillet clean and melt butter over medium heat. Add the onions, bay leaf, salt, and pepper. Cover and cook until onions are caramelized or dark golden brown – approximately 30-40 minutes, stirring occasionally. Set aside to cool slightly.
For the tart: Preheat oven to 375°F. Roll out pastry to fit a 9- or 10-inch tart pan with a removable bottom. Line the pastry with parchment paper or foil and place pie weights or beans on top of the paper. Bake to set dough – approximately 10-15 minutes. Remove paper/foil and weights. Bake until evenly golden brown – approximately another 20 minutes.
While the crust is in the oven, whip egg white. Remove the crust from the oven and while still warm, brush with the egg white to seal the crust. If the crust cools before the egg white is applied, return to oven for a minute to cook the egg white.
Reduce oven temperature to 350°F. In a medium mixing bowl, whisk the half & half, eggs, and nutmeg together. Remove the bay leaf from the onions and spread the onions evenly over the crust. Pour the cream mixture over the onions. Use the end of a fork to gently move the onions around if needed. Top with diced bacon.
Bake until the tart is set – approximately 30-40 minutes. Garnish with chives and serve warm or room temperature.