• Preheat the oven to 425°F.
  

For the crust

• Use a food processor fitted with the fine grater attachment -- or a hand held fine grater -- to grate the potatoes.  (The former is much easier!)
• As you grate the potatoes, add them to a large strainer over a big bowl. Then use your hands to squeeze as much liquid as possible.  Potatoes have a very high water content, so you'll be surprised at the quantity of liquid that you can actually "wring out" of the potatoes!
• Add the potatoes to a large mixing bowl with the egg, olive oil, tarragon, salt and a few turns of pepper.  Mix until everything is evenly incorporated.
• Gently press the potato mixture into a 10-inch pie plate, covering the bottom and sides evenly.  Place in the preheated oven for about 20 minutes -- the potatoes along the sides should be beginning to brown.  Now reduce the heat to 350 degrees F and continue cooking for about another 10 minutes, until the bottom is only slightly golden brown or dry.  Remove from the oven and turn the heat down to 325°F.
• While the crust is baking, cook the bacon in a large sauté pan and set it aside on a plate with a paper towel to drain.  (Don't clean this pan!)

For the filling

• Add the onions and garlic to the pan with the bacon grease.  Over medium heat, cook until the onions are soft and slightly caramelized, about 7 minutes.  Add the mushrooms in two batches and cook until they are nicely browned and until no liquid remains in the pan, about 10 to 15 minutes.  (If the pan is looking dry at any point before the mushrooms are cooked, add a bit of olive oil.) Deglaze the pan with the sherry and use a flat wooden spatula to scrape any delicious bits of mushroom and onion off the bottom and into the mixture.  Cook until all of the sherry has been cooked off.  Add the tarragon and season to taste with salt and pepper. (Here's How to Season to Taste.)
  
• In a medium-sized mixing bowl, whisk the eggs just until they are well-blended.  Season them with salt and pepper and set aside.
  

To assemble

• Place the cooked bacon strips in one layer over the potato crust.  Add the mushroom mixture on top of the bacon and pour the egg evenly over everything.  Sprinkle the top with the grated Gruyère cheese.
• Bake in the preheated 325°F oven just until the egg solidifies, about 30 minutes.  If the top hasn't browned, place the pie under the broiler for about 30 seconds. Cover the pie loosely with foil and let it sit for at about 20 minutes before serving.