Preheat oven to 400 degrees.
Heat 2 Tbsp. butter in a large sauté pan. Add the onions and sauté over medium heat until the onions are soft, but not brown, about 5 minutes.
Stir in 1 tsp. salt, 1/2 tsp. pepper and the fresh thyme, then add the swiss chard and continue cooking for 2 minutes more until the chard has wilted.
Set the swiss chard mixture in a colander in the sink to cool for 5 minutes, then gently press out any excess moisture.
Place the refrigerated pie crust in a 9″ pie pan. Crimp the edges of the dough to form a decorative edge, if desired.
In a medium bowl, combine the half-n-half, eggs, egg yolk, parmesan cheese, 1/2 tsp. salt and 1/2 tsp. pepper. Whisk well to combine.
Spread the chard mixture evenly in the pie shell and pour the egg mixture over the top.
Bake for 10 minutes at 400 degrees. Turn the oven down to 350 degrees and continue baking until the quiche is set and lightly browned about 15 minutes.
Cool for 10 minutes before serving.