In a food processor, combine both flours with the ground almonds, salt and thyme. Add the butter and pulse a few times, until it forms pea-sized pieces. Add the yogurt and pulse just until the dough starts coming together. Remove from the food processor.
Cut off ¼ of the dough and form into a disc to be used to cover the torte. Cover in plastic wrap. Form the remaining dough into a disc to be used as the bottom crust. Cover in plastic wrap. Refrigerate for at least 30 minutes while you prepare the filling.
Meanwhile, in a large skillet over medium heat, soften the leek in 2 tbsp of the butter. Add the wine and let reduce until almost dry. Add the cheese and stir until melted. Season with salt and pepper. Set aside.
Using a mandoline, cut the potatoes into slices 1/8 inch (3 mm) thick and place in a bowl of cold water. Cut the squash and beets on the mandoline into slices 1/8 inch (3 mm) thick and place on separate plates.
In a pot off the heat, place the potatoes (drain before using), milk, salt, thyme and garlic. Season with pepper. Bring to a boil. Simmer over medium heat for 5 minutes or until the potatoes are al dente, swirling the pot a few times to make sure the milk doesn’t stick. Using a slotted spoon, remove the potatoes and place on a large plate.
Add the squash slices to the pot of milk and bring to a boil. Add more milk, as needed, to just cover the squash. Simmer over medium heat until al dente. Drain the squash and place on a large plate. Discard the milk, thyme and garlic.
With the rack in the lowest position, preheat the oven to 400°F (200°C).
On a lightly floured work surface, roll out the larger disc of dough until 1/8 inch (3 mm) thick into a circle that’s at least 13 inches (33 cm) in diameter. Use the dough to line an 8-inch (20 cm) springform pan with removable bottom. Prick the dough all over with a fork. Roll out the smaller disc of dough into an 8-inch (20 cm) circle. Using a small ¾-inch (2 cm) round cookie cutter or pastry tip, make a hole at the centre of the circle of dough to let steam escape as the torte cooks. Set aside.
In another bowl, combine the egg and milk. Set the egg wash aside.
In a small bowl, melt the remaining ¼ cup (55 g) of butter in the microwave oven.
Scatter the leek mixture over the bottom crust. Top with the potatoes, then the squash and finally the beets. Brush each layer with melted butter as you go. Brush the edges of the bottom crust with the egg wash. Place the top dough circle over the vegetables, folding the edges of the crusts together to seal. Brush the top of the torte with egg wash.
Bake for 45 minutes or until the surface of the crust is golden. Let cool for 15 minutes before unmoulding. Serve with a salad with creamy tarragon dressing.