Preheat the oven to 325 degrees. In a large bowl, beat together the milk, cream, eggs, tarragon, salt, and pepper.
Scatter half of the grated cheese in the blind-baked crust. Top with the chopped, drained spinach and edamame. Pour over the liquid mixture. Sprinkle over the remaining cheese. Place in the oven and bake for 40 to 45 minutes until set and lightly golden.
For Pastry Crust:
Put the flour into the container of a food processor. Add the butter and pulse. When the mixture resembles coarse meal, add the egg yolk. Continue pulsing while gradually adding the water. Add enough water so that the dough will come away from the sides of the container and be firm but pliable enough to shape into a ball. Wrap the ball of dough in plastic wrap and chill for 30 minutes.
Preheat the oven to 400 degrees. Lightly flour your countertop, flatten the dough slightly, and roll it out with a rolling pin into a circle approximately 1/8-inch thick. Carefully transfer the crust to an 8-inch pie plate. Fold the dough edges over and crimp with your fingers to make a pretty edge. Refrigerate for 30 minutes.
Line the crust with parchment paper and fill it with dried beans or pie weights. Bake 10 minutes.
Remove the parchment and beans or weights. Brush very lightly with beaten egg.