Spread the pecans out on a baking sheet or pizza pan, and put them on the top shelf of the preheated oven. Keep a close eye on them, and when you note even a little darkening, remove them immediately to avoid burning (which happens alarmingly quickly). Set the pecan aside.
Melt butter in a saucepan over very low heat. Remove from the heat.
In a microwave-safe bowl, combine syrups, sugar, eggs, lemon juice, vanilla, salt, and flour. Stir well, then blend in the butter. Put the bowl in the microwave at 20 percent power for about 15 seconds. Stir again, and repeat this process until the mixture feels slightly warm to the touch and begins to get thick.
Brush the unbaked pie shell bottom with egg white. This keeps the crust from getting soggy. Pour the filling into the pie shell. Top with the pecans, pushing them down with a spoon if necessary so that all the pecans are at least touching the filling.
Bake at 350 degrees for 10 minutes, then reduce temperature to 275 degrees for 30 to 40 minutes. Cool to warm room temperature.
