Grease and flour a 8 "x 12" tart pan (preferably one with a removable bottom)
In a food processor pulse the whole wheat flour and the salt until combined.
Add the cold butter pieces and pulse until the mixture has crumbs the size of peas.
Slowly stream in the water while pulsing. Stop mixing right when the dough has formed.
Remove the dough from the food processor, pat into a ball, wrap with plastic cling film and refrigerate for 30 minutes.
Preheat the oven to 350 degrees F.
Roll out the crust on a lightly floured surface. Press into the prepared pan.
Use a fork to poke holes in the bottom of the crust.
Line a baking sheet with aluminum foil
Trim and peel the beets and rinse them. Slice the beets into thin rounds.
Place the beets on the baking sheets and brush with olive oil.
Roast for 15 minutes.
Remove from oven.
When the beets are cool enough to handle, place them in the bottom of the tart shell.
Whisk together the eggs, milk, feta and tarragon.
Season the mixture with salt and pepper.
Pour the mixture over the beets.
Bake for 45 minutes until the middle is solid (if you insert a knife, it should come out clean.)
Let cool in the pan for 10-15 minutes before slicing and serving.