Preheat broiler with oven rack 7 inches from heat.

Cook bacon in a skillet over medium heat until crisp; crumble.

Reserve 1 Tbsp. drippings.

Place red onion on a baking sheet; brush with drippings.

Broil 4 minutes per side.

Reduce oven temperature to 400°F (200°C).

Whisk together cream, salt, pepper, and eggs in a bowl.

Unfold pastry on a lightly floured surface.

Roll the puff pastry to a 12-inch square.

Fit the puff pastry into a greased 9-inch tart or quiche pan.

Sprinkle 1 cup Swiss cheese and half of the crumbled bacon onto the pastry crust.

Top with chopped green onions and broiled red onions.

Pour the cream mixture over the onions.

Fold excess dough toward the center of the tart.

Sprinkle the center with grated Parmesan cheese and the remaining crumbled bacon and Swiss cheese.

Combine egg yolk and milk in a small bowl.

Brush the egg wash over the dough.

Bake at 400°F (200°C) for 40 minutes, or until golden brown.

Let the tart stand for 10 minutes before serving.

Serve with Pea-and-Green Onion Soup (optional).