Preheat the oven to 350 degrees F (175 degrees C).

Cook bacon in a large skillet over medium-high heat, turning occasionally, until crispy, about 10 minutes. Drain on paper towels. Let cool 10 minutes, then crumble and set aside.

Roll out pastry crust using a lightly floured rolling pin to fit a 9-inch pie plate. Place crust in pie plate. Prick holes into crust bottom using a fork.

Bake in the preheated oven on the middle rack for 15 minutes.

Remove crust from the oven; brush with beaten egg. Return crust to the oven; bake 5 minutes more.

Heat butter in a pan over medium heat. Add onion; cook and stir until softened and translucent, about 5 minutes. Reduce heat to low; continue cooking and stirring until onion very tender and dark brown, about 40 minutes more.

Whisk remaining 2 eggs together in a bowl. Add sour cream and cream cheese; beat with an electric mixer until well combined. Beat in salt and pepper.

Spread caramelized onions with remaining butter onto pastry crust; sprinkle in 1/2 cup Cheddar cheese. Place crumbled bacon evenly over top; pour in egg mixture, then top with remaining 1/2 cup Cheddar cheese.

Bake quiche in the preheated oven until golden and fluffy, about 30 minutes. Let cool 10 minutes before serving.