In a standing electric mixer fitted with the paddle, combine the flour, cheese, thyme, lemon zest and salt. Add the butter and egg yolks and beat at medium speed until lightly moistened crumbs form. Gather the crumbs and knead to form a 2-inch-thick log. Wrap in plastic and refrigerate until chilled, about 30 minutes.
Preheat the oven to 325° and line 2 baking sheets with parchment. Slice the log 1/4 inch thick and arrange on the baking sheets. Bake for about 20 minutes, until golden around the edges; let cool on the sheets.
In a large pot, melt the butter. Add the onion, cover and cook over moderate heat, stirring, until softened, about 6 minutes. Add the asparagus and cook for 1 minute. Add the broth and simmer until the asparagus is tender, about 10 minutes.
Add the 1/4 cup of tarragon and the parsley. Working in batches, puree the soup in a blender. Return the soup to the pot, add the cream and peas; rewarm. Season with salt and white pepper and garnish with tarragon and zest. Serve with the Parmesan coins.