Preheat oven to 325 degrees. Pulse walnuts in a food processor until finely ground. Transfer to a bowl, and whisk in flour and 1/2 teaspoon salt.
Beat butter, sugar, and vanilla with a mixer on high speed until pale and fluffy. Reduce speed to low. Gradually beat in walnut mixture.
Divide dough into eighteen 1 1/2-inch balls, and press into irregular stone shapes using the palm of your hand; transfer to a parchment-lined baking sheet. Dust food-safe plastic insects with flour to coat; press into dough to make fossil impressions. Freeze until dough is very firm, 20 to 30 minutes.
Bake until golden brown and firm in center, 25 to 28 minutes. Transfer sheet to a wire rack, and let cool.