Make the crust: Combine the flour, salt and sugar in a large bowl. Add the butter; mix with a pastry blender or your fingers until the mixture resembles coarse crumbs. Beat the egg yolk and 3 tablespoons ice water in a small bowl; work into the dough until the dough holds together without being wet or sticky. Squeeze a small amount together: If it is crumbly, add more ice water, 1 tablespoon at a time. Form into a disk and wrap in plastic wrap; refrigerate at least 30 minutes.
Roll out the dough on a lightly floured surface into a 14-inch round. Carefully roll up the dough onto the rolling pin (this may take a little practice) and lay it inside a 9-inch springform pan. Press the dough firmly into the bottom and side; trim the excess. Put the pan on a sturdy baking sheet and refrigerate until ready to fill.
Prepare the filling: Put a skillet over medium-low heat and coat with the olive oil. Add the onions and slowly cook, stirring occasionally, until they caramelize, 40 to 45 minutes. (Add a couple of tablespoons of water to help the onions break down, if needed.) Toss in the ham and cook, stirring, about 10 minutes. Remove from the heat.
Preheat the oven to 375 degrees F. Whisk the eggs in a large bowl until frothy. Whisk in the cream; season with salt and pepper. Arrange the onions and ham in the crust and carefully pour in the egg-cream mixture; the filling should be about 1/2 inch from the top. Cover loosely with foil and bake 1 hour, 45 minutes. Remove the foil and bake until the quiche is set but jiggles slightly, about 30 more minutes. Remove to a rack and let cool 45 minutes.
Meanwhile, make the salad: Bring a large pot of salted water to a boil; blanch the asparagus until crisp-tender, about 2 minutes. Transfer to a bowl of ice water to stop the cooking, then drain. Slice into small pieces and put in a bowl; add the parmesan and herbs. Add the olive oil and lemon juice and season with salt and pepper. Toss gently to combine.
Loosen the quiche from the pan with a thin metal spatula, then remove the ring. Transfer the quiche to a plate and cut into wedges. Drizzle with olive oil and season with pepper. Top with the salad.