In the bowl of a food processor, combine the flour and salt and pulse 2 or 3 times. Add the butter and pulse until the mixture resembles a coarse meal.
In a large mixing bowl, whisk together the yogurt, water, and lemon juice. Add the flour mixture to the bowl. Using clean hands, mix everything until it comes together into a ball. Wrap in plastic and store in the refrigerator for at least 30 minutes.
In a small mixing bowl, whisk together the olive oil and garlic. Set this aside.
In a larger bowl combine the feta, ricotta, parmesan, and mozzarella cheeses as well as the fresh herbs. Stir in 1 teaspoon of the olive oil and garlic.
Preheat the oven to 400°F. Line a sheet pan with parchment paper.
On a floured work surface, roll the chilled dough into a 12-inch diameter circle, trimming the edges until smooth. Transfer the dough to the lined baking sheet. Spread the cheese mixture in the center of the dough, leaving a 2-inch border around the perimeter. Arrange the asparagus in a row over the cheese and drizzle the remaining olive oil mixture over the top.
Fold over the edges of the dough, pleating each fold over the previous one so the dough forms a rustic lip that holds the filling in place.
In a small bowl, whisk together the egg yolk and water. Brush the egg wash over the exposed crust.
Place the pan in the oven and bake for 30 minutes or until the crust is golden brown and the cheese has puffed up and the asparagus is tender.
Allow the galette to cool for about 5 minutes. Then, cut in wedges or squares and serve.