In a food processor, combine flour and salt. Add in butter and pulse until small pebbles form.
In a small bowl, combine sour cream, lemon juice, and water. Add to food processor and pulse until mixture comes together and forms dough. Wrap dough in plastic wrap and refrigerate for at least one hour, or up to two days.
Make the filling:
Bring a medium-sized saucepan of salted water to boil. Add in beets and cook until they soften, about 20-30 minutes, depending on size. Beets don't need to be cooked all the way through, but you should be able to pierce them with a fork relatively easily.
Preheat oven to 400F.
Let beets cool. Peel off skins and grate on a box grater or in a food processor. Transfer to bowl.
In a large skillet, heat olive oil. Add in onion and cook until translucent. Stir in fennel and garlic, season with salt, and cook until fennel softens.
Add fennel mixture to bowl with beets. Stir in walnuts, herbs, and sour cream.
Roll out dough into about a 12 inch round. Place vegetables in the center, leaving about a 1½ - 2 inch border around the sides. Use your hands to scatter goat cheese evenly across the top. Fold the edges of the dough in, overlapping where there is extra.
In a small bowl, whisk together egg yolk and a drop of water. Brush the dough with egg wash and sprinkle with freshly ground black pepper.
Bake for 30-40 minutes, until dough is nicely browned. Let cool for at least 15 minutes before serving.