Step 1Mix together the cake and all-purpose flours, baking soda and salt in a bowl.
Step 2Cream the butter and sugars with an electric mixer just until the butter chunks disappear. Beat in the vanilla and eggs, one at a time. Mix in the flour mixture. Stir in the pastilles.
Step 3Cover with plastic wrap and refrigerate until very cold, 1 hour or overnight.
Step 4Heat the oven to 350 degrees (convection oven) or to 375 degrees (standard oven). Line a baking sheet with parchment paper. Roll chunks of batter between your hands into balls about the size of golf balls; place on the baking sheet. Bake until the cookies are done in the center and crispy around the edges, 11 minutes. Remove to wire racks.