In a food processor, add the finely chopped herbs, flour, and salt. Pulse to combine.
Add the cold cubed butter to the food processor, pulse for a minute. The mixture will resemble coarse crumbs. After a minute, gradually add the water, one tablespoon at a time, pulsing the mixture in the food processor. The mixture will begin to stick together and form a ball of dough. Note: You may need to add one more tablespoon of water depending on flour.
Turn off the food processor, form the dough into a ball. Press the dough into a 9-inch pie dish. Work the dough with your fingers, so the crust lines the entire dish. Place the pie pan (lined with dough) in the freezer while the filling is prepared.
Preheat the oven to 375F.
For the filling: melt 2 tablespoons of butter in a skillet. Add the chopped shallots and bacon. Cook until the shallots are translucent and bacon slightly cooked. Add in the swiss chard and a pinch of salt. Cook until the chard wilts (4 minutes).
Remove from the heat.
Remove the pie pan from the freezer.
Pour the chard mixture over the cold pie crust. Crumble the feta cheese over top.
In a small bowl, whisk together the cream, eggs, and salt and pepper, to taste. Pour the egg mixture over the cheese and chard.
Bake for 40-50 minutes, until the center is firm and “springs” when touched.