In a medium bowl, mix together crushed crackers and 1/3 cup melted butter. Press mixture firmly into a 9 inch pie pan and set aside.
Heat a medium skillet over medium heat. Melt 2 tablespoons butter in skillet and saute onions until translucent and tender but not brown. Spread into prepared crust.
In a medium bowl, whisk together eggs, half-and-half, salt, and white pepper. Pour mixture over onions then sprinkle top with shredded cheese.
Bake in preheated oven for 30 minutes, until center is set. Let stand 10 minutes before serving.
