Preheat the oven to 375 degrees Fahrenheit (190 Celsius).
Line a baking sheet with parchment paper.
In a medium skillet, cook the bacon over medium-high heat, stirring frequently, until cooked through but not crisp. Transfer the bacon to a paper towel-lined plat to drain. Wipe the excess fat from the pan and add the chopped shallot (or scallions). Cook over medium-high heat, stirring for 1-2 minute, until translucent. Add the peas, season with salt and black pepper, and cook for another minute or two. Remove from the heat.
Now that the tart pastry has come out of the oven, scatter the bacon pieces over the bottom of the baked tart shell. Spread the peas and shallot over the bacon. Place the filled tart shell on the prepared baking sheet.
In a medium bowl, whisk together the heavy cream (or half and half), egg, egg yolks, mustard, cayenne, tarragon, and 1/4 teaspoon salt.
Pour the egg mixture over the bacon and vegetables in the a tart shell, filling it to the rim of the dough. Sprinkle the Parmesan evenly over the top and bake the quiche until it no longer jiggles when you shake the pan and the top is beginning to brown, about 25 minutes. Remove from the oven and let it cool slightly before serving warm or at room temperature (it is also good as leftovers the next day).
Pair with a simple green salad tossed with a classic vinaigrette and a glass of wine.