Preheat oven to 300°.
Spread walnuts on a rimmed baking sheet and toast in oven until medium golden brown, 10 to 15 minutes. -Remove baking sheet from oven and pour walnuts onto a chopping board to cool; lower oven heat to 200°.
Line 3 baking sheets with parchment paper. "Grease up with a bit of melty butter or use a no-stick spray on the parchment to make doubly sure that the meringues don’t stick," Best says. "Don’t skip this step or you will cry later."
Crush walnut halves in your hands just to break them up a little—they should be very coarse. Whip egg whites with an electric mixer until stiff, then gradually add -sugar and flour, scraping bowl every now and then. The mixture will be thick but pourable, like cake batter, and very glossy. Add vanilla and stir in the walnuts (leave behind any nut "dust").
Using two spoons, drop small mounds (about 1 heaping tablespoonful each) onto parchment. Throw into oven until dry and just beginning to delicately crack on top, 30 to 40 minutes (they should stay white). Let cool on baking sheets until completely dry.
Make ahead: Up to 2 weeks, airtight at room temperature (less if the weather is wet).